DOCSLIB.ORG

Quantum Connections

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Connections VIEWPOINT by the exponential of the classical action divided by ħ. In general, such an integral Quantum connections is not a well-defined mathematical object, because of the uncontrollably large number Sean Hartnoll, Subir Sachdev , Tadashi Takayanagi, Xie Chen, Eva Silverstein of possible configurations. However, in the low- temperature limit of charged and Julian Sonner black holes, it can be evaluated in the Theoretical high- energy and condensed- matter physics share various ideas and near- horizon region, where the classical tools. New connections between the two have been established through quantum theory shows that the spacetime becomes 1 + 1 dimensional. And the path integral information, providing exciting prospects for theoretical advances and even over these 1 + 1- dimensional spacetimes potential experimental studies. Six scientists discuss different directions of and electromagnetic fields maps exactly as research in this inter-disciplinary field. a hologram onto the low-temperature path integral of the 0 + 1- dimensional SYK model. New connections Quantum matter without quasiparticles In recent work, extensions of such mappings have led to advances in our understanding Sean Hartnoll. High- energy and Subir Sachdev. The study of compressible of the quantum behaviour of Einsteinian condensed- matter physics are organized states of electronic matter without theories of gravity, and insights into the around common fundamental concepts quasiparticle excitations began in the black- hole information paradox. such as symmetry breaking and the early 1980s, motivated by observations of renormalization group, and share core the ‘strange metal’ in copper-oxide- based Gravity and entanglement mathematical machinery including superconductors, and by the quantum Feynman diagrams and topology. This Hall state in the half-filled Landau level of Tadashi Takayanagi. The wavefunctions has led to a historically fruitful interface semiconductors in a strong magnetic field. of quantum many- body systems are between the two fields. In the last couple When quasiparticles are present, a quantum typically complicated from an algebraic of decades, two new points of connection many- body system will relax to equilibrium point of view. However, it is often possible have emerged. in response to an external perturbation in to extract a simple geometrical structure First, holographic duality has a time of the order of the mean collision from a wavefunction, namely quantum established that the classical evolution time between the quasiparticles. Without entanglement. In other words, the ‘skeleton’ of black-hole horizons precisely captures quasiparticles, equilibration proceeds of a many-body state is given by a network of the dissipative dynamics of a strongly more rapidly and in a time as short as quantum entanglement. quantum phase of matter. In recent the ‘Planckian time’ ħ/(kTB ), where Quantum entanglement also appears years, this connection has moved beyond T is the temperature of the final state. as a fundamental degree of freedom in simple correlation functions (that Remarkably, there is a solvable model of quantum gravity. The amount of quantum describe the approach to coarse-grained non- quasiparticle quantum dynamics, the entanglement is measured by a quantity thermal equilibrium) to more nuanced SYK model of electrons with all-to- all and called entanglement entropy. With observables that can probe signatures random interactions. This model displays the framework of holographic duality, of many-body quantum chaos. Tied up Planckian time relaxation and also describes entanglement entropies in conformal field with this shift has been the emergence some other aspects of the physics of the theories (CFTs) turn out to be equal to areas of the Sachdev–Ye–Kitaev (SYK) model. copper oxide superconductors. of minimal surfaces in an anti-de- Sitter This model shares many of the features A distinct physical system that also space. This holographic entanglement (and limitations) of fully fledged holographic displays Planckian time relaxation is a entropy formula was recently generalized theories, but is both microscopically closer to black hole, and this becomes clear from into CFTs coupled to a dynamical gravity, conventional condensed-matter Hamiltonians the quantum temperature of a black hole providing a remarkable explanation for the and under greater technical control. computed by Stephen Hawking in 1974. black hole information paradox. Second, many- body quantum In this case, there is a remarkable and Surprisingly, the above two observations entanglement has simultaneously emerged surprisingly close connection between in two different subjects suggest the as an organizing principle in both fields. the SYK model and black holes with a fascinating prospect that gravitational It appears that quantum states supporting net electric charge, the latter described by spacetime can emerge from quantum holographically emergent gravity have quantizing Einstein’s classical theory of entanglement. This idea has been used an entanglement structure that may gravity and Maxwell’s classical theory successfully over the past several years be analogous to that of topologically of electromagnetism. The quantization within the conventional holography non- trivial phases of matter. Fleshing out is described by a path integral over for a special class of spacetime whose this connection promises to be a source different configurations of spacetime and cosmological constant is negative. I expect of future progress. electromagnetic fields, each weighted this approach will also be crucial when NATURE REVIEWS | PHYSICS 0123456789();: VIEWPOINT trying to tackle holography for general to be possible. All these features suggest that spacetimes, including de Sitter spaces. these models cannot be properly described using a continuous field theory, at least not String theory Fracton models in the usual way. Progress has been made on many Xie Chen. In the past few years, a new aspects, including the discovery of new class of quantum many- body models, models, connecting some of the features to Quantum Quantum Black-hole called the ‘fracton’ models, has captured systems we are familiar with, and exploring information matter physics the imagination of theorists from the new conceptual ideas to properly capture condensed- matter and the high- energy the underlying order (for a review, see communities alike. These models, many REFS1,2). Yet we are only scratching the of which were discovered as quantum error surface. The exotic physics of the fracton Condensed- correction codes, host a number of exotic model may fundamentally change and matter properties never seen before. They contain extend the way we approach quantum physics point excitations that cannot move on their many- body systems, while bringing the own, the ground- state degeneracy grows quantum- information, condensed- matter Fig. 1 | Quantum connections. The study of exponentially with system size, and the usual and high- energy communities closer quantum matter lies at the intersection of four renormalization group transformation does together (Fig. 1). areas of fundamental physics, providing a fertile not apply. ground for the exchange of ideas and tools. Figure Fracton models challenge both A new notion of universality adapted with permission from REF.6, Cambridge condensed- matter and high-energy theory. University Press. The immobility of the point excitations Eva Silverstein. A classic connection results in slow and non-thermal dynamics between high- energy and condensed- matter that needs to be better understood and physics concerns the renormalization irrelevant’ phenomena that become characterized. The growing ground-state group and the related notion of universality. important in the presence of long times degeneracy indicates an order that is not The details of the microscopic theory do not or large fields. only beyond the symmetry-breaking affect the outcome of experiments involving Reversing this flow is generally paradigm but also beyond the conventional low- energy probes of a system, enabling fraught with ambiguity, since one cannot topological paradigm. The renormalization a principled focus on a small number of determine the microscopic physics from group transformation needs to be relevant terms in the Lagrangian of the a few relevant terms at low energy. But augmented with non-trivial resource states theory. There is an exception: ‘dangerously in a new development3–5, certain irrelevant deformations are solvable and universal in a new sense. These deformations are The contributors specified via a differential equation, through Sean Hartnoll is Associate Professor of Physics at Stanford University. He received his PhD from a step- by- step procedure. At each step, Cambridge University in 2005 and did postdocs at Cambridge, KITP Santa Barbara and Harvard. the Lagrangian of the theory is deformed by He won the New Horizons prize in 2015. He has co- authored a book on ‘Holographic Quantum a certain bilinear of the stress energy tensor Matter’ and works on a range of topics in high energy, gravitational and condensed matter physics. known as TT ; the effect of this tensor on the Subir Sachdev is Herchel Smith Professor of Physics at Harvard University. He was educated energy spectrum is calculable. Joining this at the Indian Institute of Technology, the Massachusetts Institute of Technology and Harvard. to a trajectory including the addition of a His honours include the Dirac Medal and the Onsager
Load more

Recommended publications
  • Graphene Reveals Its Strange Side
    VIEWPOINT Graphene Reveals Its Strange Side Experiments on magic-angle graphene reveal a ``strange metal'' phase and transport behavior consistent with so-called Planckian dissipation. by Subir Sachdev∗ with a low-temperature transport behavior called Planckian dissipation [2, 3]. The same association is found by Jarillo- agic-angle graphene captured the attention of Herrero and colleagues in magic-angle graphene, providing condensed-matter physicists in 2018 when it further evidence that strange metals are united by a funda- was discovered that this material—made of two mentally new form of transport that theorists are busy trying sheets of graphene with slightly misaligned lat- to characterize. Mtice orientations (Fig. 1)—is a superconductor. Moreover, The transport of electrical and heat currents in metals was observations showed that the phase diagram of magic- once a well-understood corner of condensed-matter physics. angle graphene is similar to that of copper oxide high- This understanding was based on the Drude formula, which temperature superconductors, with an insulating region relates the electrical conductivity to the density of mobile next to a dome-shaped superconducting region (see Trend: electrons, the mass of an electron, and the time between Bilayer Graphene’s Wicked, Twisted Road). Now, Pablo scattering events, t. The original theory, developed by Paul Jarillo-Herrero from the Massachusetts Institute of Technol- Drude in 1900, treated the electrons as classical particles and ogy, Cambridge, and his colleagues report that magic-angle largely ignored electron-electron interactions. Remarkably, graphene has another remarkable feature of the cuprate Drude’s formula survived a quantum-mechanics update in phase diagram: a “strange metal” phase in which the re- the 1930s, in which the electron mass was replaced by sistivity scales linearly with temperature down to very low the effective mass of an electronic “quasiparticle,” and the temperatures [1].
    [Show full text]
  • Institute Lecture
    Institute Lecture Quantum Mechanics Without Particles Professor Subir Sachdev Department of Physics, Harvard University . Tuesday, 21st January, 2014, Time: 6.00 PM, Venue: L-17, Lecture Hall Complex Abstract Quantum mechanics provides a thorough understanding of the physical properties of most common metals, insulators, and superconductors. Even 23 though we cannot solve the Schrödinger equation for 10 particles, we are able to make progress because the electrons move essentially independent of each other. However, in many modern materials, and particularly in the high temperature superconductors, there are important regimes where the independent-electron paradigm breaks down, and we have to deal with wave functions in which all the electrons are entangled with each other in a non- local manner. Understanding such quantum states, in which no particle-like excitations can be identified, is a major theoretical challenge. In this talk, we will describe recent progress in this field using quantum field theory, string theory, and computer simulations. These advances shed light on many of the puzzling features of phase diagrams of the high temperature superconductors. About the speaker Prof. Subir Sachdev is a distinguished condensed matter physicist. He is very well known for his research on quantum phase transitions, and its application to a variety of quantum materials, such as the high temperature superconductors. His book "Quantum Phase Transitions" (Cambridge University Press) has formed the basis of much subsequent research. More recently, he pioneered the application of string theory to the study of quantum phase transitions in condensed matter physics, such as the superfluid- insulator transition of bosons moving in a lattice.
    [Show full text]
  • (A) Ds Backgrounds from Asymmetric Orientifolds
    hep-th/0106209 SLAC-PUB-8869 NSF-ITP-01- (A)dS Backgrounds from Asymmetric Orientifolds Eva Silverstein Department of Physics and SLAC, Stanford University, Stanford, CA 94305/94309 Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 I present asymmetric orientifold models which, with the addition of RR fluxes, fix all the NS NS moduli including the dilaton. In critical string theory, this gives new AdS backgrounds with (discretely tunably) weak string coupling. Extrapolating to super- critical string theory, this construction leads to a promising candidate for a metastable de Sitter background with string coupling of order 1/10 and dS radius of order 100 times the string scale. Extrapolating further to larger and larger super-critical dimension suggests the possibility of finding de Sitter backgrounds with weaker and weaker string coupling. arXiv:hep-th/0106209v1 22 Jun 2001 This note is an updated version of the last part of my Strings 2001 talk. June 2001 1. Introduction Because of bounds on Brans-Dicke forces and on time-dependence of couplings, it is of interest to fix the moduli in string/M theory. The diverse ingredients arising in modern string backgrounds, including branes and RR fields, introduce new sources of moduli as well as new forces which can help stabilize the moduli. In 2 I will present a six-dimensional model where the NS-NS moduli (including the § dilaton) are fixed, so that there are no runaway directions in moduli space. The strategy, as outlined in the last few minutes of my Strings 2001 talk, is to balance the first few terms in string perturbation theory off of each other by introducing large flux quanta and/or brane charges, in such a way that a minimum arises in the effective potential in a controlled regime at weak string coupling.
    [Show full text]
  • Adrian Del Maestro's CV.PDF
    Adrian Del Maestro Department of Physics University of Vermont 82 University Place Burlington, VT 05405 USA Phone: 802-656-0068 Fax: 802-656-0817 Email: [email protected] URL: http://www.delmaestro.org/adrian/ Education Ph.D. in Physics, 2008. Thesis: The superconductor-metal quantum phase transition in ultra-narrow wires. Supervisor: Subir Sachdev. Harvard University, Cambridge, MA, USA M.S. in Physics, 2005 Yale University, New Haven, CT, USA M.Sc. in Physics, 2003. Thesis: Quantum spin fluctuations in the Heisenberg-like pyrochlore antiferromagnet gadolinium titanate. Supervisor: Michel Gingras. University of Waterloo, Waterloo, ON, Canada B.Sc. in Physics joint with Mathematics, 2002. Graduated summa cum laude. University of Waterloo, Waterloo, ON, Canada Professional Experience Assistant Professor of Physics University of Vermont (Burlington, VT, USA) 2011–Present Distinguished Postdoctoral Fellow Institute for Quantum Matter, Johns Hopkins University (Baltimore, MD, USA) 2010–2011 Postdoctoral Research Scientist University of British Columbia (Vancouver, BC, Canada) 2008 Research Scientist Harvard University (Cambridge, MA, USA) 2008– 2008 System Administrator Harvard University (Cambridge, MA, USA) 2006– 2008 Lab Technician University of Western Ontario, Brain Research Laboratories (London, ON, Canada) 1999 Publications (30 total, h-index: 15, citations: 597) 1. C. M. Herdman, P.-N. Roy, R.G. Melko and A. Del Maestro, Entanglement area law in superfluid 4He, Nature Phys. 4075, 1 (2017). 2. Adrian Del Maestro and Massimo Boninsegni, Absence of superfluidity in a quasi-one-dimensional parahydrogen fluid adsorbed inside carbon nanotubes, Phys. Rev. B 95, 054517 (2017). 3. C. M. Herdman, P.-N. Roy, R. G. Melko and A. Del Maestro, Spatial entanglement entropy in the ground state of the Lieb-Liniger model, Phys.
    [Show full text]
  • Shamit Kachru Professor of Physics and Director, Stanford Institute for Theoretical Physics
    Shamit Kachru Professor of Physics and Director, Stanford Institute for Theoretical Physics CONTACT INFORMATION • Administrative Contact Dan Moreau Email [email protected] Bio BIO Starting fall of 2021, I am winding down a term as chair of physics and then taking an extended sabbatical/leave. My focus during this period will be on updating my background and competence in rapidly growing new areas of interest including machine learning and its application to problems involving large datasets. My recent research interests have included mathematical and computational studies of evolutionary dynamics; field theoretic condensed matter physics, including study of non-Fermi liquids and fracton phases; and mathematical aspects of string theory. I would characterize my research programs in these three areas as being in the fledgling stage, relatively recently established, and well developed, respectively. It is hard to know what the future holds, but you can get some idea of the kinds of things I work on by looking at my past. Highlights of my past research include: - The discovery of string dualities with 4d N=2 supersymmetry, and their use to find exact solutions of gauge theories (with Cumrun Vafa) - The construction of the first examples of AdS/CFT duality with reduced supersymmetry (with Eva Silverstein) - Foundational papers on string compactification in the presence of background fluxes (with Steve Giddings and Joe Polchinski) - Basic models of cosmic acceleration in string theory (with Renata Kallosh, Andrei Linde, and Sandip Trivedi)
    [Show full text]
  • Gauge Fields, Scalars, Warped Geometry, and Strings
    SLAC-PUB-8671 December 2000 hep-th/0010144 Gauge Fields, Scalars, Warped Geometry, and Strings Eva Silverstein Department of Physics Stanford University, Stanford, CA 94305 Stanford Linear Accelerator Center Stanford University, Stanford, CA 94309 Presented at the Strings 2000 Conference, 7/10/2000—7/15/2000, Ann Arbor, MI, USA Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 Work supported by Department of Energy contract DE–AC03–76SF00515. hep-th/0010144 SLAC-PUB-8671 Gauge Fields, Scalars, Warp ed Geometry, and Strings EvaSilverstein DepartmentofPhysics and SLAC Stanford University Stanford, CA 94305/94309 We review results on several interesting phenomena in warp ed compacti cations of M theory,aspresented at Strings 2000. The b ehavior of gauge elds in dimensional reduction from d +1 to d dimensions in various backgrounds is explained from the p ointof view of the holographic duals (and a p oint raised in the question session at the conference is addressed). We summarize the role of additional elds (in particular scalar elds) in 5d warp ed geometries in making it p ossible for Poincare-invariant domain wall solutions to exist to a nontrivial order in a controlled approximation scheme without ne-tuning arXiv:hep-th/0010144 v2 19 Oct 2000 of parameters in the 5d action (and comment on the status of the singularities arising in the general relativistic description of these solutions). Finally,we discuss brie y the emergence of excitations of wrapp ed branes in warp ed geometries whose e ective thickness, as measured along the Poincare slices in the geometry, grows as the energy increases.
    [Show full text]
  • Quantum Conductors in a Plane
    Proc. Natl. Acad. Sci. USA Vol. 96, pp. 9983–9984, August 1999 From the Academy This paper is a summary of a session presented at the tenth annual symposium on Frontiers of Science, held November 19–21, 1998, at the Arnold and Mabel Beckman Center of the National Academies of Sciences and Engineering in Irvine, CA. Quantum conductors in a plane PHILIP PHILLIPS*†,SUBIR SACHDEV‡,SERGEY KRAVCHENKO§, AND ALI YAZDANI* *Loomis Laboratory of Physics, University of Illinois at Urbana-Champaign, 1100 West Green Street, Urbana, IL 61801-3080; ‡Department of Physics, P.O. Box 208120, Yale University, New Haven, CT 06520; and §Department of Physics, Northeastern University, Boston, MA 02115 When electrons are confined to move in a plane, strange things not a sufficient condition for superconductivity. If one envi- happen. For example, under normal circumstances, they are sions dividing a material into partitions, insulating behavior not expected to conduct electricity at low temperatures. The obtains if each partition at each snapshot in time has the same absence of electrical conduction in two dimensions (2D) at number of Cooper pairs. That is, the state is static. However, zero temperature has been one of the most cherished para- if the number of pairs fluctuates between partitions, transport digms in solid-state physics (1). In fact, the 1977 physics Nobel of Cooper pairs is possible and superconductivity obtains. Prize was awarded, in part, for the formulation of the basic The fundamental physical principle that drives all quantum principle on which this result is based. However, recent phase transitions is quantum uncertainty or quantum entan- experiments (2) on a dilute electron gas confined to move at glement.
    [Show full text]
  • Condensed Matter and Ads/CFT 3 Tems, Almost All of Which Are Not Exactly Solvable
    Condensed matter and AdS/CFT Subir Sachdev Lectures at the 5th Aegean summer school, “From gravity to thermal gauge the- ories: the AdS/CFT correspondence”, Adamas, Milos Island, Greece, September 21-26, 2009, and the De Sitter Lecture Series in Theoretical Physics 2009, University of Groningen, November 16-20, 2009. Abstract I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspon- dence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I de- scribe how relativistic structures arise in models of physical interest, present re- sults for their quantum critical crossover functions and magneto-thermoelectric hy- drodynamics. The second class concerns symmetry breaking transitions of two- dimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scal- ing structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS du- als. arXiv:1002.2947v1 [hep-th] 16 Feb 2010 Subir Sachdev Department of Physics, Harvard University, Cambridge MA 02138, e-mail: [email protected] 1 2 Subir Sachdev 1 Introduction The past couple of decades have seen vigorous theoretical activity on the quantum phases and phase transitions of correlated electron systems in two spatial dimen- sions. Much of this work has been motivated by the cuprate superconductors, but the list of interesting materials continues to increase unabated [1].
    [Show full text]
  • New Horizons in Quantum Matter Physics Next: from Quantum Fields to Condensed Matter
    New Horizons in Quantum Matter Physics Next: From Quantum Fields to Condensed Matter Hyatt Place Long Island Hotel, NY Aug 24-26, 2017 Subir Sachdev Talk online: sachdev.physics.harvard.edu HARVARD Quantum condensed matter physics before the 1980s: The ground state of metals and insulators is adiabatically connected to the free electron state Excitations are electron-like quasiparticles Pairing of electrons into Cooper pairs, and their condensation leads to superconductivity Breaking of symmetry describes superconductivity, ferromagnetism, antiferromagnetism, and other ordered states Hints of physics beyond quasiparticles: the Wilson-Fisher theory of the Ising transition at finite temperature, the theory of dynamic critical phenomena, Nozieres-Blandin multi- channel Kondo critical point Quantum condensed matter physics before the 1980s: The ground state of metals and insulators is adiabatically connected to the free electron state Excitations are electron-like quasiparticles Pairing of electrons into Cooper pairs, and their condensation leads to superconductivity Breaking of symmetry describes superconductivity, ferromagnetism, antiferromagnetism, and other ordered states Hints of physics beyond quasiparticles: the Wilson-Fisher theory of the Ising transition at finite temperature, the theory of dynamic critical phenomena, Nozieres-Blandin multi- channel Kondo critical point VOI vM+ $5s +vMQ&R PHYSIC:AI. REVIEW LETTERS 11 AvGvsY 1980 ew et od for High-Accuracy Determination of th e Fine--Structure Constant Based on Quantized Hall Resistance K. v. Klitzing Hsysikalisches Institut der Universitat Wurzburg, D-8700 ~iirgburg,urgburg, FederalI'ederal RepublicRe b of Germany, and IIochfeld-Ma gn etlabor des Max-Planckx- anc --Insnstitutstitut pier PestkorPerforsckung, P 38048-Grenoble, Prance G. Dorda Forschungslaboratorien der Siemens AG, D-80000 Mununcken,ThePedera/ integerRePublic of quantumGermany Hall effect and VOI vM+ $5s +vMQ&R PHYSIC:AI.
    [Show full text]
  • Topological Order, Emergent Gauge Fields, and Fermi Surface
    arXiv:1801.01125 Topological order, emergent gauge fields, and Fermi surface reconstruction Subir Sachdev Department of Physics, Harvard University, Cambridge MA 02138, USA Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5 Department of Physics, Stanford University, Stanford CA 94305, USA E-mail: [email protected] December 2017 Abstract. This review describes how topological order associated with the presence of emergent gauge fields can reconstruct Fermi surfaces of metals, even in the absence of translational symmetry breaking. We begin with an introduction to topological order using Wegner's quantum Z2 gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying Z2 magnetic flux. The interplay between topological order and the breaking of global symmetry is described by the non-zero temperature statistical mechanics of classical XY models in dimension D = 3; such models also describe the zero temperature quantum phases of bosons with short-range interactions on the square lattice at integer filling. The topological state is again characterized by the expulsion of certain defects, in a state with fluctuating symmetry-breaking order, along with the presence of emergent gauge fields. The phase diagrams of the Z2 gauge theory and the XY models are obtained by embedding them in U(1) gauge theories, and by studying their Higgs and confining phases. These ideas are then applied to the single-band Hubbard model on the square lattice. A SU(2) gauge theory describes the fluctuations of spin-density-wave order, and its phase diagram is presented by analogy to the XY models.
    [Show full text]
  • Type IIA D-Branes, K-Theory and Matrix Theory Petr Hofava A
    © 1998 International Press Adv. Theor. Math. Phys. 2 (1998) 1373-1404 Type IIA D-Branes, K-Theory and Matrix Theory Petr Hofava a a California Institute of Technology, Pasadena, CA 91125, USA horava@theory. caltech. edu Abstract We show that all supersymmetric Type IIA D-branes can be con- structed as bound states of a certain number of unstable non-supersym- metric Type IIA D9-branes. This string-theoretical construction demon- strates that D-brane charges in Type IIA theory on spacetime manifold X are classified by the higher K-theory group K_1(X), as suggested recently by Witten. In particular, the system of N DO-branes can be obtained, for any iV, in terms of sixteen Type IIA D9-branes. This sug- gests that the dynamics of Matrix theory is contained in the physics of magnetic vortices on the worldvolume of sixteen unstable D9-branes, described at low energies by a £7(16) gauge theory. e-print archive: http://xxx.lanl.gov/abs/hep-th/9812135 1374 TYPE 11 A D-BRANES, K-THEORY, AND MATRIX THEORY 1 Introduction When we consider individual D-branes in Type IIA or Type IIB string theory on R10, we usually require that the branes preserve half of the original su- persymmetry, and that they carry one unit of the corresponding RR charge. These requirements limit the D-brane spectrum to p-branes with all even values of p in Type IIA theory, and odd values of p in Type IIB theory. Once we relax these requirements, however, we can consider Dp-branes with all values of p.
    [Show full text]
  • Joseph Gerard Polchinski Jr Physicists Around the World
    Joseph Gerard Polchinski Jr Physicists around the world mourned the death of Joseph Gerard Polchinski Jr. He died on 2 February 2018 in Santa Barbara, California, after having battled brain cancer since late 2015. Joe is widely regarded as one of the leading theorists of recent decades. His contributions ranged from an exact prescription for the renormalization group to the discovery of central ingredients in string theory. Along the way he offered major insights into condensed‐matter physics, the cosmological constant, and the quantum physics of black holes. Joe is fondly remembered for his good‐ natured, informal style and his support of new generations of physicists. His mischievous grin and ready laugh lit up his surroundings.. He recalled a desire to name one of his most famous papers “Fun with duality,” only to have it vetoed by his supposedly much more serious graduate‐student coauthor. Readers can learn about his perspective on physics and beyond in his recent memoir (https://arxiv.org/abs/1708.09093), in which he recalls the people and circumstances surrounding many of his results. Born in White Plains, New York, on 16 May 1954, Joe developed his focus on physics at Caltech, where he obtained his BS in 1975. He earned his 1980 PhD from the University of California, Berkeley, with a dissertation, ʺVortex operators in gauge field theories,ʺ supervised by Stanley Mandelstam. He then moved to a two‐year postdoc at SLAC. Joeʹs work began to have real significance to the physics community during his second postdoc, at Harvard University. There, starting from an insight of Kenneth Wilson that the couplings in quantum field theories depend on the scale at which they are probed, he proceeded to give an exact prescription for calculating the dependence.
    [Show full text]