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CERN Courier January/February 2017 Quantum and unification Gravity’s quantum side

Theoretical has arrived at crossroads, with no clues so far as to what lies beyond or the . If we are ever to break through this impasse, we need to borrow from Einstein’s epochal feats.

There is little doubt that, in spite of their overwhelm- ing success in describing phenomena over a vast range of distances, general relativity (GR) and the Standard Model (SM) of are incomplete theo- ries. Concerning the SM, the problem is often cast in terms of the remaining open issues in particle physics, such as its failure to account for the origin of the mat- Vecto_CERN Courier_193x125.indd 1 12/12/2016 09:23:06 ter– asymmetry or the nature of dark . But the real problem with the SM is theoretical: it is not clear whether it makes sense at all as a beyond perturba- tion theory, and these doubts extend to the whole framework Progress of of quantum fi eld theory (QFT) (with perturbation theory as the main tool to extract quantitative predictions). The occurrence of Theoretical and “ultraviolet” (UV) divergences in Feynman diagrams, and the need for an elaborate mathematical procedure called renormalisa- tion to remove these infinities and make testable predictions order- by-order in perturbation theory, strongly point to the necessity of A slice Progress of Theoretical and Experimental Physics is a some other and more complete theory of elementary particles. through the On the GR side, we are faced with a similar dilemma. Like the root of the fully open access, online-only journal. SM, GR works extremely well in its domain of applicability and group E10, a possible has so far passed all experimental tests with flying colours, most symmetry for . Each point is associated with Read our latest Special Section: recently and impressively with the direct detection of gravitational one or more independent symmetry operations – similar to the waves (see p21). Nevertheless, the need for a theory beyond Ein- fl avour SU(3) root diagram for the meson octet, but vastly more Nambu, A Foreteller of III stein is plainly evident from the existence of space–time singulari- complicated. There are infi nitely many such layers, and the This Special Section is based on a symposium ties such as those occurring inside black holes or at the moment of number of symmetry operations grows exponentially as one the . Such singularities are an unavoidable consequence penetrates deeper and deeper into the E10 Lie algebra. held at the University of Chicago in memory of of Einstein’s equations, and the failure of GR to provide an answer (Image credit: T Nutma.) Professor . calls into question the very conceptual foundations of the theory. Unlike quantum theory, which is rooted in probability and Applying conventional particle-physics wisdom to Einstein’s uncertainty, GR is based on notions of smoothness and geom- theory by quantising small fluctuations of the metric (cor- academic.oup.com/ptep etry and is therefore subject to classical determinism. Near a responding to gravitational waves) cannot help either, since it pro- space–time singularity, however, the description of space–time duces non-renormalisable infinities that undermine the predictive as a continuum is expected to break down. Likewise, the assump- power of perturbatively quantised GR. tion that elementary particles are point-like, a cornerstone of In the face of these problems, there is a wide consensus that the QFT and the reason for the occurrence of ultraviolet infinities outstanding problems of both the SM and GR can only be over- ▲ in the SM, is expected to fail in such extreme circumstances. come by a more complete and deeper theory: a theory of quantum

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CERNCOURIER www. V o l u m e 5 7 N u m b e r 1 J a n u ary /F e b r u a r y 2 0 1 7 CERN Courier January/February 2017 CERN Courier January/February 2017 Quantum gravity and unification Quantum gravity and unification

to try to emulate Einstein’s epochal feat of creating a new theory The success of symmetry has fuelled hopes that we temperature 32 27 15 13 out of purely theoretical considerations. of 10 K10 K10 K10 K3 K might ultimately understand the evolution of the universe from its beginning as a symmetry-breaking Emulating Einstein cascade, where at each step more and more of the Yet, after more than 40 years of unprecedented collective intel- strong force initial symmetry is lost as the universe expands and lectual effort, different points of view have given rise to a growing electromagnetic force cools down. In this view, the unsymmetrical world that j3 j3 diversification of approaches to QG – with no convergence in sight. weak force we see around us is only the broken phase of a highly It seems that has arrived at crossroads, with symmetrical theory at the origin of the universe, when nature remaining tight-lipped about what comes after Einstein gravity forces, matter and space–time were unified into a j2 and the SM. There is currently no evidence whatsoever for any of single entity. However, this picture has so far been the numerous QG schemes that have been proposed – no signs of time after –43 –35 –12 –6 17 validated only up to scales accessible to the j1 10 s10 s10 s10 s5 × 10 s −18 low-energy , large or “stringy” Big Bang ( = now) LHC, or equivalently distances down to 10 cm. j1 j2 excitations have been seen at the LHC so far. The situation is no better for approaches that do not even attempt to make predictions or “canonical” approaches, the main unsolved problems concern graphic entanglement, as advocated by AdS/CFT aficionados? that could be tested at the LHC. the emergence of classical space–time and the Einstein fi eld There is cer tainly no lack of enticing ideas, but without a firm guid- If quantum space is made of web-like structures (spin networks), Existing approaches to QG fall roughly into two catego- equations in the semiclassical limit, and their inability to recover ing principle and the prospect of making a falsifiable prediction, as postulated by LQG-like approaches, a describes ries, refl ecting a basic schism that has developed in the com- standard QFT results such as anomalies. On the other side, a main such speculations may well end up in the nirvana of undecidable the quantum evolution of such spin networks in time. In the munity. One is based on the assumption that Einstein’s theory shortcoming is the “background dependence” of the quantisation propositions and untestable expectations. abstract description, the ambient space–time in which the spin can stand on its own feet, even when confronted with quantum procedure, for which both and have to Why then consider unification? Perhaps the strongest argument in foam is “embedded” is simply not there, since all of the . This would imply that QG is nothing more than the rely on perturbative expansions about some given space–time favour of unification is that the underlying principle of symmetry has resides on the spin foam. non-perturbative quantisation of Einstein’s theory and that GR, background geometry. In fact, in its presently known form, string so far guided the development of modern physics from Maxwell’s suitably treated and eventually complemented by the SM, cor- theory cannot even be formulated without reference to a specific theory to GR all the way to Yang–Mills and the SM (see gravity (QG) that possibly unifi es gravity with the other fundamental rectly describes the physical degrees of freedom also at the very space–time background. diagram above). It is therefore reasonable to suppose that unification interactions in nature. But how are we to approach this challenge? smallest distances. The earliest incarnation of this approach goes These fundamentally different viewpoints also offer different and symmetry may also point the way to a consistent theory of QG. back to the pioneering work of John Wheeler and Bryce DeWitt in perspectives on how to address the non-renormalisability of Ein- This point of view is reinforced by the fact that the SM, although Planck-scale physics the early 1960s, who derived a GR analogue of the Schrödinger stein’s theory, and consequently on the need (or not) for unification. only a partially unified theory, does already afford glimpses of trans- Unlike with , whose development was driven equation in which the “wave function of the universe” encodes Supergravity and try to eliminate the infinities of Planckian physics, independently of whether new physics shows up by the need to explain observed phenomena such as the existence the entire information about the universe as a quantum system. the perturbatively quantised theory, in particular by including fer- at the LHC or not. This is because the requirements of renormalis- of spectral lines in , nature gives us very few hints of Alas, the non-renormalisable infi nities resurface in a different mionic matter in Einstein’s theory, thus providing a raison d’être for ability and vanishing gauge anomalies put very strong constraints on where to look for QG effects. One main obstacle is the sheer small- guise: the Wheeler–DeWitt equation is so ill-defined mathemati- the existence of matter in the world. They therefore automatically the particle content of the SM, which are indeed in perfect agreement ness of the , of the order 10−33 cm, which is the scale cally that no one until now has been able to make sense of it arrive at some kind of unification of gravity, space–time and matter. with what we see in detectors. There would be no more convincing at which QG effects are expected to become visible (conversely, in beyond mere heuristics. More recent variants of this approach in By contrast, canonical approaches attribute the ultraviolet infinities vindication of a theory of QG than its ability to predict the matter terms of energy, the relevant scale is 1019 GeV, which is 15 orders of the framework of (LQG), spin foams and to basic deficiencies of the perturbative treatment. However, to rec- content of the world (see panel overleaf). magnitude greater than the energy range accessible to the LHC). group fi eld theory replace the space–time metric by new vari- oncile this view with , they will have to invoke There is no hope of ever directly measuring genuine QG effects in ables (Ashtekar variables, or holonomies and fl uxes) in a renewed some mechanism – a version of Weinberg’s asymptotic safety – to In search of SUSY the laboratory: with zillions of in even the weakest burst attempt to overcome the mathematical diffi culties. save the theory from the abyss of non-renormalisability. Among the promising ideas that have emerged over the past dec- of gravitational waves, realising the gravitational analogue of the The opposite attitude is that GR is only an effective low-energy ades, arguably the most beautiful and far reaching is supersym- will forever remain a dream. theory arising from a more fundamental Planck-scale theory, Conceptual challenges metry. It represents a new type of symmetry that relates bosons One can nevertheless speculate that QG might manifest itself whose basic degrees of freedom are very different from GR or Beyond the mathematical diffi culties to formulating QG, there are and fermions, thus unifying forces (mediated by vector bosons) indirectly, for instance via measurable features in the cosmic quantum fi eld theory. In this view, GR and space–time itself are a host of issues of a more conceptual nature that are shared by all with matter (quarks and leptons), and which endows space–time microwave background, or cumulative effects originating from assumed to be emergent, much like macroscopic physics emerges approaches. Perhaps the most important concerns the very ground with extra fermionic dimensions. Supersymmetry is very natural a more granular or “foamy” space–time. Alternatively, perhaps from the quantum world of and . The perceived rules of quantum mechanics: even if we could properly define and from the point of view of cancelling divergences because bosons a framework will emerge that provides a compelling explanation need to replace Einstein’s theory by some other and more funda- solve the Wheeler–DeWitt equation, how are we to interpret the and fermions generally contribute with opposite signs to loop dia- for inflation, and the origin of the universe. Although mental theory, having led to the development of supersymmetry resulting wave function of the universe? After all, the latter pretends grams. This aspect means that low-energy (N = 1) supersymmetry not completely hopeless, available proposals typically do not and supergravity, is the basic hypothesis underlying superstring to describe the universe in its entirety, but in the absence of out- can stabilise the electroweak scale with regard to the Planck scale, allow one to unambiguously discriminate between very different theory (see p41). Superstring theory is the leading contender for a side classical observers, the Copenhagen interpretation of quantum thereby alleviating the so-called via the cancel- approaches, for instance when contrarian schemes like string the- perturbatively fi nite theory of QG, and widely considered the most mechanics clearly becomes untenable. On a slightly less grand scale, lation of quadratic divergences. These models predict the existence ory and loop quantum gravity vie to explain features of the early promising possible pathway from QG to SM physics. This approach there are also unresolved issues related to the possible loss of infor- of a mir ror world of super par tners that differ from the SM par ticles universe. And even if evidence has spawned a hugely varied set of activities and produced many mation in connection with the Hawking evaporation of black holes. only by their opposite statistics (and their ), but otherwise have for new effects was found in, important ideas. Most notable among these, the AdS/CFT corre- A fur ther question that any theory of QG must eventually answer identical internal quantum numbers. say, cosmic-ray physics, these spondence posits that the physics that takes place in some volume concerns the texture of space–time at the Planck scale: do there To the great disappointment of many, experimental searches at All of the important might very well admit conven- can be fully encoded in the surface bounding that volume, as for a exist “space–time atoms” or, more specifically, web-like struc- the LHC so far have found no evidence for the superpartners pre- questions remain tional explanations. hologram, and consequently that QG in the bulk should be equiva- tures like spin networks and spin foams, as claimed by LQG-like dicted by N = 1 supersymmetry. However, there is no reason to give wide open. In the search for a consistent lent to a pure quantum fi eld theory on its boundary. approaches? (see diagram on previous page) Or does the space– up on the idea of supersymmetry as such, since the refutation of theory of QG, it therefore seems Apart from numerous technical and conceptual issues, there time continuum get dissolved into a gas of strings and branes, as low-energy supersymmetry would only mean that the most simple- ▲ that we have no other choice but remain major questions for all approaches to QG. For LQG-like suggested by some variants of string theory, or emerge from holo- minded way of implementing this idea does not work. Indeed, the

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to try to emulate Einstein’s epochal feat of creating a new theory The success of symmetry has fuelled hopes that we temperature 32 27 15 13 out of purely theoretical considerations. of universe 10 K10 K10 K10 K3 K might ultimately understand the evolution of the universe from its beginning as a symmetry-breaking Emulating Einstein cascade, where at each step more and more of the Yet, after more than 40 years of unprecedented collective intel- strong force initial symmetry is lost as the universe expands and lectual effort, different points of view have given rise to a growing electromagnetic force cools down. In this view, the unsymmetrical world that j3 j3 diversification of approaches to QG – with no convergence in sight. weak force we see around us is only the broken phase of a highly It seems that theoretical physics has arrived at crossroads, with symmetrical theory at the origin of the universe, when nature remaining tight-lipped about what comes after Einstein gravity forces, matter and space–time were unified into a j2 and the SM. There is currently no evidence whatsoever for any of single entity. However, this picture has so far been the numerous QG schemes that have been proposed – no signs of time after –43 –35 –12 –6 17 validated only up to energy scales accessible to the j1 10 s10 s10 s10 s5 × 10 s −18 low-energy supersymmetry, or “stringy” Big Bang ( = now) LHC, or equivalently distances down to 10 cm. j1 j2 excitations have been seen at the LHC so far. The situation is no better for approaches that do not even attempt to make predictions or “canonical” approaches, the main unsolved problems concern graphic entanglement, as advocated by AdS/CFT aficionados? that could be tested at the LHC. the emergence of classical space–time and the Einstein fi eld There is cer tainly no lack of enticing ideas, but without a firm guid- If quantum space is made of web-like structures (spin networks), Existing approaches to QG fall roughly into two catego- equations in the semiclassical limit, and their inability to recover ing principle and the prospect of making a falsifiable prediction, as postulated by LQG-like approaches, a spin foam describes ries, refl ecting a basic schism that has developed in the com- standard QFT results such as anomalies. On the other side, a main such speculations may well end up in the nirvana of undecidable the quantum evolution of such spin networks in time. In the munity. One is based on the assumption that Einstein’s theory shortcoming is the “background dependence” of the quantisation propositions and untestable expectations. abstract description, the ambient space–time in which the spin can stand on its own feet, even when confronted with quantum procedure, for which both supergravity and string theory have to Why then consider unification? Perhaps the strongest argument in foam is “embedded” is simply not there, since all of the geometry mechanics. This would imply that QG is nothing more than the rely on perturbative expansions about some given space–time favour of unification is that the underlying principle of symmetry has resides on the spin foam. non-perturbative quantisation of Einstein’s theory and that GR, background geometry. In fact, in its presently known form, string so far guided the development of modern physics from Maxwell’s suitably treated and eventually complemented by the SM, cor- theory cannot even be formulated without reference to a specific theory to GR all the way to Yang–Mills theories and the SM (see gravity (QG) that possibly unifi es gravity with the other fundamental rectly describes the physical degrees of freedom also at the very space–time background. diagram above). It is therefore reasonable to suppose that unification interactions in nature. But how are we to approach this challenge? smallest distances. The earliest incarnation of this approach goes These fundamentally different viewpoints also offer different and symmetry may also point the way to a consistent theory of QG. back to the pioneering work of John Wheeler and Bryce DeWitt in perspectives on how to address the non-renormalisability of Ein- This point of view is reinforced by the fact that the SM, although Planck-scale physics the early 1960s, who derived a GR analogue of the Schrödinger stein’s theory, and consequently on the need (or not) for unification. only a partially unified theory, does already afford glimpses of trans- Unlike with quantum mechanics, whose development was driven equation in which the “wave function of the universe” encodes Supergravity and superstring theory try to eliminate the infinities of Planckian physics, independently of whether new physics shows up by the need to explain observed phenomena such as the existence the entire information about the universe as a quantum system. the perturbatively quantised theory, in particular by including fer- at the LHC or not. This is because the requirements of renormalis- of spectral lines in atomic physics, nature gives us very few hints of Alas, the non-renormalisable infi nities resurface in a different mionic matter in Einstein’s theory, thus providing a raison d’être for ability and vanishing gauge anomalies put very strong constraints on where to look for QG effects. One main obstacle is the sheer small- guise: the Wheeler–DeWitt equation is so ill-defined mathemati- the existence of matter in the world. They therefore automatically the particle content of the SM, which are indeed in perfect agreement ness of the Planck length, of the order 10−33 cm, which is the scale cally that no one until now has been able to make sense of it arrive at some kind of unification of gravity, space–time and matter. with what we see in detectors. There would be no more convincing at which QG effects are expected to become visible (conversely, in beyond mere heuristics. More recent variants of this approach in By contrast, canonical approaches attribute the ultraviolet infinities vindication of a theory of QG than its ability to predict the matter terms of energy, the relevant scale is 1019 GeV, which is 15 orders of the framework of loop quantum gravity (LQG), spin foams and to basic deficiencies of the perturbative treatment. However, to rec- content of the world (see panel overleaf). magnitude greater than the energy range accessible to the LHC). group fi eld theory replace the space–time metric by new vari- oncile this view with semiclassical gravity, they will have to invoke There is no hope of ever directly measuring genuine QG effects in ables (Ashtekar variables, or holonomies and fl uxes) in a renewed some mechanism – a version of Weinberg’s asymptotic safety – to In search of SUSY the laboratory: with zillions of gravitons in even the weakest burst attempt to overcome the mathematical diffi culties. save the theory from the abyss of non-renormalisability. Among the promising ideas that have emerged over the past dec- of gravitational waves, realising the gravitational analogue of the The opposite attitude is that GR is only an effective low-energy ades, arguably the most beautiful and far reaching is supersym- photoelectric effect will forever remain a dream. theory arising from a more fundamental Planck-scale theory, Conceptual challenges metry. It represents a new type of symmetry that relates bosons One can nevertheless speculate that QG might manifest itself whose basic degrees of freedom are very different from GR or Beyond the mathematical diffi culties to formulating QG, there are and fermions, thus unifying forces (mediated by vector bosons) indirectly, for instance via measurable features in the cosmic quantum fi eld theory. In this view, GR and space–time itself are a host of issues of a more conceptual nature that are shared by all with matter (quarks and leptons), and which endows space–time microwave background, or cumulative effects originating from assumed to be emergent, much like macroscopic physics emerges approaches. Perhaps the most important concerns the very ground with extra fermionic dimensions. Supersymmetry is very natural a more granular or “foamy” space–time. Alternatively, perhaps from the quantum world of atoms and molecules. The perceived rules of quantum mechanics: even if we could properly define and from the point of view of cancelling divergences because bosons a framework will emerge that provides a compelling explanation need to replace Einstein’s theory by some other and more funda- solve the Wheeler–DeWitt equation, how are we to interpret the and fermions generally contribute with opposite signs to loop dia- for inflation, dark energy and the origin of the universe. Although mental theory, having led to the development of supersymmetry resulting wave function of the universe? After all, the latter pretends grams. This aspect means that low-energy (N = 1) supersymmetry not completely hopeless, available proposals typically do not and supergravity, is the basic hypothesis underlying superstring to describe the universe in its entirety, but in the absence of out- can stabilise the electroweak scale with regard to the Planck scale, allow one to unambiguously discriminate between very different theory (see p41). Superstring theory is the leading contender for a side classical observers, the Copenhagen interpretation of quantum thereby alleviating the so-called hierarchy problem via the cancel- approaches, for instance when contrarian schemes like string the- perturbatively fi nite theory of QG, and widely considered the most mechanics clearly becomes untenable. On a slightly less grand scale, lation of quadratic divergences. These models predict the existence ory and loop quantum gravity vie to explain features of the early promising possible pathway from QG to SM physics. This approach there are also unresolved issues related to the possible loss of infor- of a mir ror world of super par tners that differ from the SM par ticles universe. And even if evidence has spawned a hugely varied set of activities and produced many mation in connection with the Hawking evaporation of black holes. only by their opposite statistics (and their mass), but otherwise have for new effects was found in, important ideas. Most notable among these, the AdS/CFT corre- A fur ther question that any theory of QG must eventually answer identical internal quantum numbers. say, cosmic-ray physics, these spondence posits that the physics that takes place in some volume concerns the texture of space–time at the Planck scale: do there To the great disappointment of many, experimental searches at All of the important might very well admit conven- can be fully encoded in the surface bounding that volume, as for a exist “space–time atoms” or, more specifically, web-like struc- the LHC so far have found no evidence for the superpartners pre- questions remain tional explanations. hologram, and consequently that QG in the bulk should be equiva- tures like spin networks and spin foams, as claimed by LQG-like dicted by N = 1 supersymmetry. However, there is no reason to give wide open. In the search for a consistent lent to a pure quantum fi eld theory on its boundary. approaches? (see diagram on previous page) Or does the space– up on the idea of supersymmetry as such, since the refutation of theory of QG, it therefore seems Apart from numerous technical and conceptual issues, there time continuum get dissolved into a gas of strings and branes, as low-energy supersymmetry would only mean that the most simple- ▲ that we have no other choice but remain major questions for all approaches to QG. For LQG-like suggested by some variants of string theory, or emerge from holo- minded way of implementing this idea does not work. Indeed, the

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been seen, duality have turned out to be ubiquitous in Einstein on unifi cation supergravity and string theory, and they also reveal a fascinating and unsuspected link with the so-called exceptional Lie groups. It is well known that spent much of the latter part of his life The LHC’s extra dimension More recently, hints of an enormous symmetry enhancement have vainly searching for unification, although disregarding the nuclear forces also appeared in a completely different place, namely the study of and certainly with no intention of reconciling quantum mechanics and GR. cosmological solutions of Einstein’s equations near a space-like Already in 1929, he published a paper on the unified theory (pictured below). singularity. This mathematical analysis has revealed tantalising In this paper, he states with wonderful and characteristic lucidity what the evidence of a truly exceptional infinite-dimensional duality sym- criteria should be of a “good” unified theory: to describe as far as possible all metry, which goes by the name of E10, and which “opens up” as one The discovery of additional space–time phenomena and their inherent links, and to do so on the basis of a minimal gets close to the cosmological (Big Bang) singularity (see image number of assumptions and logically independent basic concepts. The p27). Could it be that the near-singularity limit can tell us about the dimensions would revolutionise physics, but second of these goals (also known as the principle of Occam’s razor) refers underlying symmetries of QG in a similar way as the high-energy to “logical unity”, and goes on to say: “Roughly but truthfully, one might say: limit of gauge theories informs us about the symmetries of the SM? after 20 years of dedicated searches at particle we not only want to understand how nature works, but we are also after the One can validly argue that this huge and monstrously complex sym- colliders, we have turned up empty handed. perhaps utopian and presumptuous goal of understanding why nature is the metry knows about maximal supersymmetry and the way it is and not otherwise.” finite-dimensional dualities identified so far. Equally important, and unlike conventional supersymmetry, E10 may continue to make At 10.00 a.m. on 9 August 2016, gathered at the Sheraton sense in the Planck regime where conventional notions of space and hotel in Chicago for the “Beyond the Standard Model” session at time are expected to break down. For this reason, duality symmetry the ICHEP conference. The mood was one of slight disappoint- could even supersede supersymmetry as a unifying principle. ment. An excess of “diphoton” events at a mass of 750 GeV reported by the LHC’s ATLAS and CMS in 2015 had not Outstanding questions shown up in the 2016 data, ending a burst of activity that saw some Our summary, then, is very simple: all of the important questions 540 papers uploaded to the arXiv preprint server in QG remain wide open, despite a great deal of effort and numer- in a period of just eight months. Among the proposed explanations An extract from Einstein’s 1929 paper in which he set out his ous promising ideas. In the of this conclusion, the LHC will for the putative new high-mass resonance were extra space–time approach to unifi cation. (From a contribution to a continue to play a crucial role in advancing our understanding of dimensions, an idea that has been around since Theodor Kaluza commemorative publication for Aurel Stodola, Zurich, 1929.) how everything fits together, no matter what the final outcome of and Oscar Klein attempted to unify the electromagnetic and gravi- the experiments will be. This is especially true if nature chooses tational forces a century ago. not to abide by current theoretical preferences and expectations. In the modern language of string theory, extra dimensions are initial excitement about supersymmetry in the 1970s had nothing to Over the past decades, we have learnt that the SM is a most eco- required to ensure the mathematical consistency of the theory. do with the hierarchy problem, but rather because it offered a way nomical and tightly knit structure, and there is now mounting evi- They are typically thought to be very small, close to the Planck The presence of a large extra dimension could produce a clear to circumvent the so-called Coleman–Mandula no-go – a dence that minor modifi cations may suffi ce for it to survive to the length (10 –35 m). In the 1990s, however, theorists trying to solve missing-energy signal in the LHC detectors, as shown here for beautiful possibility that is precisely not realised by the models cur- highest . To look for such subtle deviations will therefore problems with supersymmetry suggested that some of these extra an ATLAS event recorded in 2011 with a missing transverse rently being tested at the LHC. be a main task for the LHC in the years ahead. If our view of the dimensions could be as large as 10–19 m, corresponding to an energy energy of 523 GeV. In fact, the reduplication of internal quantum numbers predicted Planck scale remains unobstructed by intermediate scales, the pop- scale in the TeV range. In 1998, as proposed by Arkani-Hamed and by N = 1 supersymmetry is avoided in theories with extended ular model-builders’ strategy of adding ever more unseen particles co-workers, theories emerged with even larger extra dimensions, scale was a game changer. from experiments at the LEP, (N > 1) supersymmetry. Among all supersymmetric theories, max- and couplings may come to an end. In that case, the challenge of which predicted detectable effects in contemporary collider exper- and HERA colliders quickly produced tailored searches imal N = 8 supergravity stands out as the most symmetric. Its sta- explaining the structure of the low-energy world from a Planck- iments. In such large extra-dimension (LED) scenarios, gravity can for signals for this new beyond-the-Standard Model (SM) physics tus with regard to perturbative fi niteness is still unclear, although scale theory of quantum gravity looms larger than ever. become stronger than we perceive in 3D due to the increased space scenario. No evidence was found in their accumulated data, setting recent work has revealed amazing and unexpected cancellations. available. In addition to showing us an entirely different view of the lower limits on the scale of extra dimensions of around 1 TeV. However, there is one very strange agreement between this theory Résumé universe, extra dimensions offer an elegant solution to the so-called By the turn of the century, a number of possible new experimental and observation, fi rst emphasised by Gell-Mann: the number of La face quantique de la gravité hierarchy problem, which arises because the Planck scale (where signatures had been identifi ed for extra-dimension searches, many spin-1/2 fermions remaining after complete breaking of supersym- gravity becomes as strong as the other three forces) is 17 orders of of which were studied in detail while assessing the physics perfor- metry is 48 = 3 × 16, equal to the number of quarks and leptons La physique théorique est à la croisée des chemins, et nul ne sait magnitude larger than the electroweak scale. mance of the LHC experiments. For the case of LEDs, where gravity (including right-handed neutrinos) in three generations (see p41). pour l’instant ce qui se trouve au-delà de la relativité générale ou Particle physicists normally ignore gravity because it is feeble is the only force that can expand in these dimensions, high-energy To go beyond the partial matching of quantum numbers achieved du Modèle standard. Il est admis que nous ne pourrons progresser compared with the other three collider experiments were just one approach. Smaller “tabletop” so far will, however, require some completely new insights, espe- qu’avec une théorie plus complète de la gravité quantique, forces. In theories where grav- scale experiments aiming to measure the strength of gravity at sub- cially concerning the emergence of chiral gauge interactions. qui unifi erait peut-être la gravité avec les autres interactions ity gets stronger at small dis- millimetre distances were also in pursuit of extra dimensions, but Then again, perhaps supersymmetry is not the end of the story. fondamentales de la nature. Or, après plus de 40 ans d’un effort The possibility of tances due to the opening of no deviation from the Newtonian law has been observed to date. In There is plenty of evidence that another type of symmetry may be intellectuel collectif sans précédent, les approches de la gravité having extra space extra dimensions, however, it addition, there were also signifi cant constraints from equally important, namely duality symmetry. The first example quantique sont toujours plus diversifi ées et aucune convergence dimensions at the can catch up and lead to phe- processes on the possible number and size of these dimensions. of such a symmetry, electromagnetic duality, was discovered by n’est en vue. Si nous voulons sortir un jour de cette impasse, nous nomena at colliders with high Dirac in 1931. He realised that Maxwell’s equations in vacuum devrons nous inspirer des prouesses historiques d’Einstein. TeV scale was a enough rates that they can be Enter the LHC are under rotations of the electric and magnetic fields game changer. measured in experiments. The Analysis strategies to search for extra dimensions have been into one another – an insight that led him to predict the existence Hermann Nicolai, Institute for Gravitational Physics, Potsdam, possibility of having extra deployed from the beginning of high-energy LHC operations in ▲ of magnetic monopoles. While magnetic monopoles have not Germany. space dimensions at the TeV 2010, and the recent increase in the LHC’s collision energy to

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