DOCSLIB.ORG

Emergent Gravity from Hidden Sectors and TT Deformations

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Emergent Gravity from Hidden Sectors and TT Deformations Preprint typeset in JHEP style - HYPER VERSION CCTP-2020-11 ITCP-2020/11 DCPT-20/15 Emergent gravity from hidden sectors and TT deformations ♮ ♭,♮ ♭, P. Betzios , E. Kiritsis , V. Niarchos † ♮ APC, AstroParticule et Cosmologie, Universit´eParis Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris Cit´e, 10, rue Alice Domon et L´eonie Duquet, 75205 Paris Cedex 13, France. ♭ Crete Center for Theoretical Physics, Institute for Theoretical and Computational Physics, Department of Physics University of Crete, Heraklion, Greece † Department of Mathematical Sciences and Centre for Particle Theory, Durham University, Durham DH1 3LE, UK Abstract: We investigate emergent gravity extending the paradigm of the AdS/CFT correspondence. The emergent graviton is associated to the (dynamical) expectation value of the energy-momentum tensor. We derive the general effective description of such dynamics, and apply it to the case where a hidden theory gen- erates gravity that is coupled to the Standard Model. In the linearized description, generically, such gravity is massive with the presence of an extra scalar degree of arXiv:2010.04729v2 [hep-th] 3 Nov 2020 freedom. The propagators of both the spin-two and spin-zero modes are positive and well defined. The associated emergent gravitational theory is a bi-gravity theory, as is (secretly) the case in holography. The background metric on which the QFTs are defined, plays the role of dark energy and the emergent theory has always as a solution the original background metric. In the case where the hidden theory is holographic, the overall description yields a higher-dimensional bulk theory coupled to a brane. The effective graviton on the brane has four-dimensional characteristics both in the UV and IR and is always massive. Keywords: Emergent gravity, quantum gravity, cosmological constant, holography, dark energy. Contents 1. Introduction and results 2 1.1 Results 8 1.2 Outlook 14 2. A general setup for emergent gravity 17 3. The effective action for the emergent graviton: a simple example 19 3.1 Gapped theories 23 3.2 The linearized induced interaction 27 4. Linearized emergent gravity from a hidden sector 30 4.1 Integrating-in a metric in perturbation theory 31 4.2 The induced gravitational interaction 41 4.3 IR massive gravity actions 45 4.4 Generalization to arbitrary interactions 47 4.5 Features of the emergent linearised effective theory 48 5. The non-linear theory and diffeomorphism invariance 49 6. The low-energy emergent gravitational dynamics 54 6.1 A simpler example 57 7. The holographic hidden QFT 59 8. Discussion 66 Acknowledgements 75 Appendix 76 A. Defining the stress energy correlators 76 A.1 The T Tˆ interactiononanarbitrarybackground 78 B. Ward identities and the energy-momentum two-point function 81 C. Translational invariance constraints on the Schwinger functional 84 D. Conservation of energy momentum and the emergent metric 87 E. The calculation of the effective action 89 –1– F. Linearised analysis of the effective action and equations 92 F.1 The linearized analysis in the case of a single theory 92 F.2 The linearized analysis of the T Tˆ deformation 98 F.2.1 Matching the fluctuation equations 101 F.3 The Schwinger functional and the effective action at the linearized level102 G. Solutions to the effective Einstein equation of a single theory 108 G.1 Einstein manifolds 108 G.2 General spherically symmetric ansatz 108 G.2.1 Perturbation theory 110 G.2.2 Secondorderperturbationtheory 113 G.3 Cosmological solutions 115 G.4 Conformally flat Cosmology 117 H. Inverting a general stress energy two-point function 118 I. The spectral representation of the stress-tensor two-point function122 I.1 Renormalization in momentum space 124 I.2 The static potential 129 I.3 Improvements 129 J. The Energy-momentum two-point function of free fields 130 J.1 Free bosons 130 J.2 Free fermions 134 J.3 The correlator in real space 135 J.4 The static potential 139 References 140 1. Introduction and results There is a widespread belief among experts that gravity remains todate the weak link in our attempts to understand the universe. On one hand, in many contexts (cosmology, black holes), gravity and quantum mechanics seem to give results that violently clash against each other. On the other hand, in all the cases in which only one, or the other of these frameworks seems relevant (as in gravitational physics in the solar system, or particle physics at terrestrial experiments) both theories pass tests with flying colors. Both gravity and the gauge theories that describe all the known interactions, are theories that rely on local symmetries. It is not understood why this is so. It has –2– been advocated that this fact may not be an accident, [1]. However, the similarity stops at that point: gauge theories can be UV complete theories1, while the theory of Einstein gravity is non-renormalizable. In the case of gauge theories, we can say more. If we decree that experiment commands vector fields to mediate interactions, and that vector fields are good dy- namical variables all the way to the UV (i.e.. weakly coupled), then we know that their interactions must be controlled by a gauge theory (possibly spontaneously bro- ken). Sometimes, a similar argument can also be made for composite low-energy vectors, as is the case near the lower end of the conformal window in N=1 sQCD, [28]. Many different proposals have been put forward in the past in an effort to over- come the UV problems of gravity and which are reviewed in [2, 3, 4]. One particular set of ideas involves the concept of “emergent gravity” which is quite vague and has many different incarnations, [5]-[17]. This is to be contrasted with the concept of induced gravity pioneered by Sakharov, [18] and reviewed in [19, 20]. In this second line of thought, the graviton is a priori a dynamical field that is coupled to “mat- ter”. It is however the matter that determines the gravitational action via Wilsonian renormalization and quantum effects. It is reasonable to have a definition of emergent gravity as the theory where the graviton is a composite of the “fundamental” fields of the theory. This definition can become confusing when dualities are at play. Indeed, dualities relate two theories written in terms of different “fundamental” degrees of freedom. However, in most cases this is a good working definition. Therefore from this point of view, and in contrast with induced gravity, the emergent graviton is not a fundamental field at high energy, but only an effective low-energy field. In many cases, it emerges in the context of standard relativistic quantum field theory (QFT). There are however non-relativistic approaches, typically inspired by condensed matter theories with or without an explicit cutoff, where a low-energy graviton is claimed to emerge, [21]-[24]. Perturbative string theory, is a case that shares some features of the emergence phenomenon. The standard NSR description of the theory has dynamical fields (the coordinates of the string) that do not involve directly the space-time metric. The theory however, has explicit invariance under space-time diffeomorphisms2. In retrospect, a dynamical space-time metric (and many other fields) emerge in the theory, making it a quantum theory of gravity. String theory, at the same time does something, other approaches to quantiz- ing gravity cannot do. It provides a perturbatively well-defined theory of quantum gravity that is semiclassical3. 1Modulo complications with interactions mediated by scalars. 2And world-sheet diffeomorphisms as well. 3In the limit of weak coupling, where we know how to handle the theory. –3– String theory4 provides a quantized theory of gravity at a cost: it introduces an infinite number of “new” degrees of freedom, the excited states of the string and 1 a scale, the string scale M ℓ− at which these new states become effective, and s ∼ s resolve some of the problems of the gravitational and other interactions. The theory of strings is UV-finite but not UV-complete. The structure of closed string perturbation theory suggests a theory with a smart cutoff at the string scale, containing therefore no UV divergences (but plenty of IR divergences), [25]. Pertur- bative string theories are well-defined for energies well below the Planck scale, but ill-defined at energy transfers at or above the Planck scale where string perturbation theory breaks down, [26, 27]5. The presence of a non-renormalizable interaction in an effective QFT is not new in the field. We have two well-known, and historically important cases, whose resolution taught us interesting lessons. The first is the Fermi interaction. Its non- renormalizability was resolved by introducing new degrees of freedom (the W and Z bosons) and a related mass scale. In a sense, for gravity, string theory comes somewhat close (but is not identical) to this paradigm. It introduces new degrees of freedom and “resolves” the gravitational interaction. The new scale, Ms, is related 8 to the Planck scale MP of the non-renormalizable gravitational interaction as Ms = g2M 8 . In the perturbative formulation therefore we always find M M . s P s ≪ P Another idea that is in a sense similar, is the approach of quantizing gravity starting with an R2 Lagrangian, [29, 30, 31]. In that case, renormalizability is ensured by a new degree of freedom that is a ghost. Recently, modifications of this formalism have been proposed, [32, 33], but it is not clear yet, what is their interpretation. The other example is QCD. Here, at low energy we have a non-renormalizable IR-free theory of pions. Its characteristic scale is the pion decay constant, fπ, and it is analogous to the Planck scale in the gravity example.
Load more

Recommended publications
  • Arxiv:1911.13166V1 [Hep-Th] 29 Nov 2019
    Composite Gravitons from Metric-Independent Quantum Field Theories∗ Christopher D. Caroney High Energy Theory Group, Department of Physics, William & Mary, Williamsburg, VA 23187-8795 (Dated: December 2, 2019) Abstract We review some recent work by Carone, Erlich and Vaman on composite gravitons in metric- independent quantum field theories, with the aim of clarifying a number of basic issues. Focusing on a theory of scalar fields presented previously in the literature, we clarify the meaning of the tunings required to obtain a massless graviton. We argue that this formulation can be interpreted as the massless limit of a theory of massive composite gravitons in which the graviton mass term is not of Pauli-Fierz form. We then suggest closely related theories that can be defined without such a limiting procedure (and hence without worry about possible ghosts). Finally, we comment on the importance of finding a compelling ultraviolet completion for models of this type, and discuss some possibilities. arXiv:1911.13166v1 [hep-th] 29 Nov 2019 ∗ Invited Brief Review for Modern Physics Letters A. [email protected] 1 I. INTRODUCTION A quantum field may represent a fundamental degree of freedom, or a composite state described within the context of an effective theory that is applicable in a low-energy regime. The idea that the gauge fields of the standard model may not be fundamental has appeared periodically in the literature over the past 50 years [1{3]. Such models must have a gauge invariance even when no gauge fields are included ab initio. Of particular interest to us here are models like those described in Ref.
    [Show full text]
  • Einstein's Geometrical Versus Feynman's Quantum
    universe Review Einstein’s Geometrical versus Feynman’s Quantum-Field Approaches to Gravity Physics: Testing by Modern Multimessenger Astronomy Yurij Baryshev Astronomy Department, Mathematics & Mechanics Faculty, Saint Petersburg State University, 28 Universitetskiy Prospekt, 198504 St. Petersburg, Russia; [email protected] or [email protected] Received: 17 August 2020; Accepted: 7 November 2020; Published: 18 November 2020 Abstract: Modern multimessenger astronomy delivers unique opportunity for performing crucial observations that allow for testing the physics of the gravitational interaction. These tests include detection of gravitational waves by advanced LIGO-Virgo antennas, Event Horizon Telescope observations of central relativistic compact objects (RCO) in active galactic nuclei (AGN), X-ray spectroscopic observations of Fe Ka line in AGN, Galactic X-ray sources measurement of masses and radiuses of neutron stars, quark stars, and other RCO. A very important task of observational cosmology is to perform large surveys of galactic distances independent on cosmological redshifts for testing the nature of the Hubble law and peculiar velocities. Forthcoming multimessenger astronomy, while using such facilities as advanced LIGO-Virgo, Event Horizon Telescope (EHT), ALMA, WALLABY, JWST, EUCLID, and THESEUS, can elucidate the relation between Einstein’s geometrical and Feynman’s quantum-field approaches to gravity physics and deliver a new possibilities for unification of gravitation with other fundamental quantum physical interactions.
    [Show full text]
  • Soft Collinear Effective Theory for Gravity
    Soft collinear effective theory for gravity Takemichi Okui and Arash Yunesi Department of Physics, Florida State University, 77 Chieftain Way, Tallahassee, FL 32306, USA Abstract We present how to construct a Soft Collinear Effective Theory (SCET) for gravity at the leading and next-to-leading powers from the ground up. The soft graviton theorem and decou- pling of collinear gravitons at the leading power are manifest from the outset in the effective symmetries of the theory. At the next-to-leading power, certain simple structures of amplitudes, which are completely obscure in Feynman diagrams of the full theory, are also revealed, which greatly simplifies calculations. The effective lagrangian is highly constrained by effectively mul- tiple copies of diffeomorphism invariance that are inevitably present in gravity SCET due to mode separation, an essential ingredient of any SCET. Further explorations of effective theories of gravity with mode separation may shed light on lagrangian-level understandings of some of the surprising properties of gravitational scattering amplitudes. A gravity SCET with an ap- arXiv:1710.07685v3 [hep-th] 16 Feb 2018 propriate inclusion of Glauber modes may serve as a powerful tool for studying gravitational scattering in the Regge limit. Contents 1 Introduction 2 2 Building up gravity SCET 3 2.1 Fundamentals . .3 2.1.1 The target phase space . .3 2.1.2 Manifest power counting . .4 2.1.3 Other underlying assumptions . .5 2.2 The collinear lightcone coordinates . .5 2.3 Mode separation and scaling . .6 2.3.1 The collinear momentum scaling . .6 2.3.2 The cross-collinear scaling and reparametrization invariance (RPI) .
    [Show full text]
  • Composite Gravity from a Metric-Independent Theory of Fermions
    Composite gravity from a metric-independent theory of fermions Christopher D. Carone∗ and Joshua Erlichy High Energy Theory Group, Department of Physics, College of William and Mary, Williamsburg, VA 23187-8795 Diana Vamanz Department of Physics, University of Virginia, Box 400714, Charlottesville, VA 22904, USA (Dated: April 5, 2019) Abstract We present a metric-independent, diffeomorphism-invariant model with interacting fermions that contains a massless composite graviton in its spectrum. The model is motivated by the supersym- metric D-brane action, modulated by a fermion potential. The gravitational coupling is related to new physics at the cutoff scale that regularizes UV divergences. We also speculate on possible extensions of the model. ∗[email protected] [email protected] [email protected] 1 I. INTRODUCTION In Refs. [1, 2], we presented a generally covariant model of scalar fields in which gravity appears as an emergent phenomenon in the infrared. The theory requires a physical cutoff that regularizes ultraviolet divergences, and the Planck scale is then related to the cutoff scale. The existence of a massless graviton pole in a two-into-two scattering amplitude was demonstrated nonperturbatively by a resummation of diagrams, that was made possible by working in the limit of a large number of physical scalar fields φa, for a = 1 :::N. Although that work assumed a particular organizing principle, namely that the theory could be obtained from a different starting point where an auxiliary metric field is eliminated by imposing a constraint that the energy-momentum tensor of the theory vanishes, one could have just as easily started directly with the resulting non-polynomial action D v ! 2 −1 N D−1 ! Z D − 1 u D 2 u X a a X I J S = d x t det @µφ @νφ + @µX @νX ηIJ ; (1.1) V (φa) a=1 I;J=0 where D is the number of spacetime dimensions and V (φa) is the scalar potential.
    [Show full text]
  • Abstract a Natural Extension of Standard Warped Higher
    ABSTRACT Title of dissertation: A NATURAL EXTENSION OF STANDARD WARPED HIGHER-DIMENSIONAL COMPACTIFICATIONS: THEORY AND PHENOMENOLOGY Sungwoo Hong, Doctor of Philosophy, 2017 Dissertation directed by: Professor Kaustubh Agashe Department of Physics Warped higher-dimensional compactifications with \bulk" standard model, or their AdS/CFT dual as the purely 4D scenario of Higgs compositeness and par- tial compositeness, offer an elegant approach to resolving the electroweak hierar- chy problem as well as the origins of flavor structure. However, low-energy elec- troweak/flavor/CP constraints and the absence of non-standard physics at LHC Run 1 suggest that a \little hierarchy problem" remains, and that the new physics underlying naturalness may lie out of LHC reach. Assuming this to be the case, we show that there is a simple and natural extension of the minimal warped model in the Randall-Sundrum framework, in which matter, gauge and gravitational fields propagate modestly different degrees into the IR of the warped dimension, resulting in rich and striking consequences for the LHC (and beyond). The LHC-accessible part of the new physics is AdS/CFT dual to the mecha- nism of \vectorlike confinement", with TeV-scale Kaluza-Klein excitations of the gauge and gravitational fields dual to spin-0,1,2 composites. Unlike the mini- mal warped model, these low-lying excitations have predominantly flavor-blind and flavor/CP-safe interactions with the standard model. In addition, the usual leading decay modes of the lightest KK gauge bosons into top and Higgs bosons are sup- pressed. This effect permits erstwhile subdominant channels to become significant.
    [Show full text]
  • Arxiv:2101.09203V1 [Gr-Qc] 22 Jan 2021 a Powerful Selection Principle Can Be Implemented by Mation Behavior (Sec.III)
    Coordinate conditions and field equations for pure composite gravity Hans Christian Ottinger¨ ∗ ETH Z¨urich,Department of Materials, CH-8093 Z¨urich,Switzerland (Dated: January 25, 2021) Whenever an alternative theory of gravity is formulated in a background Minkowski space, the conditions characterizing admissible coordinate systems, in which the alternative theory of gravity may be applied, play an important role. We here propose Lorentz covariant coordinate condi- tions for the composite theory of pure gravity developed from the Yang-Mills theory based on the Lorentz group, thereby completing this previously proposed higher derivative theory of gravity. The physically relevant static isotropic solutions are determined by various methods, the high-precision predictions of general relativity are reproduced, and an exact black-hole solution with mildly singular behavior is found. I. INTRODUCTION As the composite theory of gravity [9], just like the underlying Yang-Mills theory, is formulated in a back- Only two years after the discovery of Yang-Mills theo- ground Minkowski space, the question arises how to char- ries [1], it has been recognized that that there is a strik- acterize the \good" coordinate systems in which the the- ing formal relationship between the Riemann curvature ory may be applied. This characterization should be tensor of general relativity and the field tensor of the Lorentz invariant, but not invariant under more general Yang-Mills theory based on the Lorentz group [2]. How- coordinate transformations, that is, it shares the formal ever, developing this particular Yang-Mills theory into a properties of coordinate conditions in general relativity. consistent and convincing theory of gravity is not at all However, the unique solutions obtained from Einstein's straightforward.
    [Show full text]
  • INTERNATIONAL CENTRE for THEORETICAL PHYSICS V
    •' ••'••'** \. IC/82/18U INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS v CCMPOSITE GRAVITY MD COMPOSITE SUPERGRAVITY Jerzy Lukierski INTERNATIONAL ATOMIC ENERGY AGENCY UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION 1982MIRAMARE-TRIESTE IC/82/1&U International Atomic Energy Agency and United nations Educational Scientific and Cultural Organization INTERNATIOHAL CESTKE FOR THEORETICAL PHYSICS COMPOSITE GRAVITY. AHD COMPOSITE SUPERGHAVITY * Jeray Lukierski *• International Centre for Theoretical Physics, Trieste, Italy. - TRIESTE September 1982 • Talk given at XIth International Colloquium on Group-Theoretic Methods in Physics, Istanbul, Turkey, 23-28 August 1982. •* Permanent address: Institute for Theoretical Physics, University of Wroclaw, ul. Cybulskiego 36, Wroclav, Poland. The known examples of such a construction are the composite U(n) ( 3) 5 potentials obtained from lj(n" "^jn,) o-fields " >, sp(l) « SU{3) ABSTRACT composite gauge fields in HP(n) a-raodels °>'T\ or eo(8) gauge fields constructed from ^Trhrr o-fields describing scalar sector of N = 8 It is known that the composite YM K-t;aui;e theory can supergravity be constructed from a-flelds taking values in a sym- metric Riemannian space — . We extend such a frame- h 2. Such a scheme can be supersymmetrized in three ways . The first work to graded o-fields taking values in supercosets. already known way is obtained by supersymmetric extension of the space- We show that from supereoset a-fields one can con- time co-ordinates, i.e. by the replacement of o-fields by a-superfields. struct composite gravity, and from supercoset a- In such a formulation the composite gauge superfields are defined 1 superfields the composite- supergravity models.
    [Show full text]
  • Mathematical Structure and Physical Content of Composite Gravity in Weak-Field Approximation
    Research Collection Journal Article Mathematical structure and physical content of composite gravity in weak-field approximation Author(s): Öttinger, Hans Christian Publication Date: 2020-09-15 Permanent Link: https://doi.org/10.3929/ethz-b-000441983 Originally published in: Physical Review D 102(6), http://doi.org/10.1103/PhysRevD.102.064024 Rights / License: Creative Commons Attribution 4.0 International This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library PHYSICAL REVIEW D 102, 064024 (2020) Mathematical structure and physical content of composite gravity in weak-field approximation Hans Christian Öttinger * ETH Zürich, Department of Materials, CH-8093 Zürich, Switzerland (Received 29 May 2020; accepted 17 August 2020; published 9 September 2020) The natural constraints for the weak-field approximation to composite gravity, which is obtained by expressing the gauge vector fields of the Yang-Mills theory based on the Lorentz group in terms of tetrad variables and their derivatives, are analyzed in detail within a canonical Hamiltonian approach. Although this higher derivative theory involves a large number of fields, only a few degrees of freedom are left, which are recognized as selected stable solutions of the underlying Yang-Mills theory. The constraint structure suggests a consistent double coupling of matter to both Yang-Mills and tetrad fields, which results in a selection among the solutions of the Yang-Mills theory in the presence of properly chosen conserved currents. Scalar and tensorial coupling mechanisms are proposed, where the latter mechanism essentially reproduces linearized general relativity. In the weak-field approximation, geodesic particle motion in static isotropic gravitational fields is found for both coupling mechanisms.
    [Show full text]
  • Background-Independent Composite Gravity
    Background-Independent Composite Gravity Austin Batz,1, ∗ Joshua Erlich,1, y and Luke Mrini1, z 1High Energy Theory Group, Department of Physics, William & Mary, Williamsburg, VA 23187-8795, USA (Dated: November 12, 2020) Abstract We explore a background-independent theory of composite gravity. The vacuum expectation value of the composite metric satisfies Einstein's equations (with corrections) as a consistency condition, and selects the vacuum spacetime. A gravitational interaction then emerges in vacuum correlation functions. The action remains diffeomorphism invariant even as perturbation theory is organized about the dynamically selected vacuum spacetime. We discuss the role of nondynamical clock and rod fields in the analysis, the identification of physical observables, and the generalization to other theories including the standard model. arXiv:2011.06541v1 [gr-qc] 12 Nov 2020 ∗[email protected] [email protected] [email protected] 1 I. INTRODUCTION Diffeomorphism invariance is responsible for a number of conceptual and technical chal- lenges for quantum gravity. The Hamiltonian in diffeomorphism-invariant theories vanishes in the absence of a spacetime boundary, and is replaced by a constraint. In canonical quan- tum gravity [1], the functional Schr¨odingerequation is replaced by the Wheeler-DeWitt equation, which imposes the Hamiltonian constraint on states. The absence of an a priori notion of time evolution in such a description suggests a relational approach to dynamics in which a clock is identified from within the system under investigation [2]. The challenge of identifying a clock with which to describe dynamics in quantum gravity is the well-known problem of time [3]. Also related to diffeomorphism invariance is the puzzle of identifying observables.
    [Show full text]
  • Mathematical Structure and Physical Content of Composite Gravity in Weak-Field Approximation
    PHYSICAL REVIEW D 102, 064024 (2020) Mathematical structure and physical content of composite gravity in weak-field approximation Hans Christian Öttinger * ETH Zürich, Department of Materials, CH-8093 Zürich, Switzerland (Received 29 May 2020; accepted 17 August 2020; published 9 September 2020) The natural constraints for the weak-field approximation to composite gravity, which is obtained by expressing the gauge vector fields of the Yang-Mills theory based on the Lorentz group in terms of tetrad variables and their derivatives, are analyzed in detail within a canonical Hamiltonian approach. Although this higher derivative theory involves a large number of fields, only a few degrees of freedom are left, which are recognized as selected stable solutions of the underlying Yang-Mills theory. The constraint structure suggests a consistent double coupling of matter to both Yang-Mills and tetrad fields, which results in a selection among the solutions of the Yang-Mills theory in the presence of properly chosen conserved currents. Scalar and tensorial coupling mechanisms are proposed, where the latter mechanism essentially reproduces linearized general relativity. In the weak-field approximation, geodesic particle motion in static isotropic gravitational fields is found for both coupling mechanisms. An important issue is the proper Lorentz covariant criterion for choosing a background Minkowski system for the composite theory of gravity. DOI: 10.1103/PhysRevD.102.064024 I. INTRODUCTION composition rule expresses the corresponding gauge vector fields in terms of the tetrad or vierbein variables providing Einstein’s general theory of relativity may not be the a Cholesky-type decomposition of a metric. As a conse- final word on gravity.
    [Show full text]
  • The Fundamental Process of Energy a Qualitative Unification of Energy, Mass, and Gravity
    The Fundamental Process of Energy A Qualitative Unification of Energy, Mass, and Gravity Conrad Ranzan 2013 www.CellularUniverse.org Reprint of the article published in two parts in Infinite Energy Magazine issue #113 (Jan/Feb 2014) and issue #114 (Mar/Apr 2014) (www.infinite-energy.com) [I]f the ultimate model of physics is to be as simple as possible, then one should expect that all the features of our universe must at some level emerge purely from properties of space. –Stephen Wolfram, A New Kind of Science 1 [T]here must be, at the bottom of it all, not an equation, but an utterly simple idea. –John A. Wheeler Abstract: The Universe is built upon a two-faceted Primary-Cause process, which serves as the key to the fundamental process of energy. Positive and negative energy processes are defined and used to resolve the cause-of-mass question, the cause-of-gravitation mystery, the dark matter problem, the vacuum energy confusion, the energy-balance misunderstanding, and the source-energy enigma. “The Fundamental Process of Energy” presents a qualitative understanding and conceptual unification of energy, mass, and gravity. Keywords: energy; energy process; positive energy; negative energy; radiation; mass; gravitation; vacuum energy; dark energy; dark matter; source energy; cosmology; DSSU theory. Grasp the significance of the key process, understand In the ninth year following the discovery of its universality, and your view of energy will never be the A the DSSU another piece of the cosmic puzzle fell into same. place —the challenge of conceptual unification of energy was resolved. As a scientific term, energy is defined simply as the 1.
    [Show full text]
  • Perturbative Methods for Superconformal Quantum Field Theories in String – Gauge Theory Dualities
    Perturbative Methods for Superconformal Quantum Field Theories in String – Gauge Theory Dualities Konstantin Wiegandt1 Centre for Research in String Theory School of Physics and Astronomy Queen Mary University of London Mile End Road, London E1 4NS, UK p3 p2 x2 p1 x1 p4 p1 x3 xn ... pi = xi xi +1 − p5 ... pn x4 x5 This review covers a number of applications of conformal field theory meth- ods for perturbative calculations in N = 4 super Yang-Mills and ABJM theory. After motivating the role of superconformal symmetry for elemen- tary particle physics research, we review some basic facts about conformal symmetry and conformal transformations of fields in a pedagogical man- ner. The implications for perturbative quantum field theory calculations are discussed in terms of Ward identities. Recent developments and rela- tions between amplitudes, correlators and Wilson loops are reviewed for N = 4 super Yang-Mills as well as ABJM theory. We give more details on arXiv:1212.5181v1 [hep-th] 20 Dec 2012 previously published results on light-like polygonal Wilson loops in ABJM theory as well as the calculation of three-point functions of two BPS and one twist-two operator in N = 4 SYM theory. This review is based on the author’s PhD thesis and includes develop- ments until April 2012. [email protected] Superconformal Quantum Field Theories in String – Gauge Theory Dualities Dissertation zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.) im Fach Physik eingereicht an der Mathematisch-Naturwissenschaftlichen Fakult¨atI der Humboldt-Universit¨atzu Berlin von Herrn Dipl.-Phys. Konstantin Wiegandt Pr¨asident der Humboldt-Universit¨atzu Berlin: Prof.
    [Show full text]