DOCSLIB.ORG

Collective Coordinates for D-Branes 1 Introduction

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Collective Coordinates for D-Branes 1 Introduction View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server UTTG-01-96 Collective Co ordinates for D-branes Willy Fischler, Sonia Paban and Moshe Rozali Theory Group, Department of Physics University of Texas, Austin, Texas 78712 Abstract We develop a formalism for the scattering o D-branes that includes collective co- ordinates. This allows a systematic expansion in the string coupling constant for such pro cesses, including a worldsheet calculation for the D-brane's mass. 1 Intro duction In the recent developments of string theory, solitons play a central role. For example, in the case of duality among various string theories, solitons of a weakly coupled string theory b ecome elementary excitations of the dual theory [1]. Another example, among many others, is the role of solitons in resolving singularities in compacti ed geometries, as they b ecome light[2]. In order to gain more insight in the various asp ects of these recent developments, it is imp ortant to understand the dynamics of solitons in the context of string theory.In this quest one of the to ols at our disp osal is the use of scattering involving these solitons. This includes the scattering of elementary string states o these solitons as well as the scattering among solitons. An imp ortant class of solitons that have emerged are D-branes [4]. In an in uential pap er [3]itwas shown that these D-branes carry R R charges, and are therefore a central ingredient in the aforementioned dualities. These ob jects are describ ed by simple conformal eld theories, which makes them particularly suited for explicit calculations. In this pap er we use some of the preliminary ideas ab out collective co ordinates de- velop ed in a previous pap er [5], to describ e the scattering of elementary string states o D-branes. We clarify and expand these ideas, providing a complete analysis of this pro cess. Research supp orted in part by the Rob ert A. WelchFoundation and NSF Grant PHY 9511632 The pap er b egins by reviewing the presence of non-lo cal violations of conformal in- variance that are a consequence of the existence of translational zero mo des. It is then shown how the world sheet theory removes these anomalies through the intro duction of collective co ordinates (which app ear as \wormhole parameters"), and the inclusion of the contribution of disconnected worldsheets to the S-matrix elements. As a bypro duct of this analysis we calculate the mass of the soliton by a purely worldsheet approach (that is amenable to higher order corrections). We thereby recover a result obtained in [4] using e ectivelow energy considerations. These ideas are then applied to the example of a closed string state scattering o a 0-brane. We showhow to include the recoil of the brane, and discover the interpretation of the wormhole parameters as collective co ordinates. The conclusion contains some comments on higher order corrections to scattering and to mass renormalization as well as p ossible extensions of this work in di erent directions. 2 Conformal anomalies. D-branes placed at di erent lo cations in space have the same energy. This implies the existence of spacetime zero mo des, one for each spatial direction transverse to the D-brane (i.e. one for each Dirichlet direction). Because of these zero mo des, the attempts to calculate scattering matrix elements in a weak coupling expansion encounter spacetime infra-red divergences. In p oint-like eld theory these divergences arise from zero mo des propagating in Feynman diagrams (for example diagrams as in Fig. 1 , where is a zero 0 mo de). Fig. 1: Diagram containing the propagation of a zero-mo de. 2 Such b ehavior can also b e found in the canonical formalism, where it manifests itself by the presence of vanishing energy denominators, characteristic of degenerate p erturbation theory. This is resolved in quantum eld theory by the intro duction of collective co ordi- nates. The right basis of states, in which the degeneracies are lifted, are the eigenstates of momenta conjugate to these co ordinates. In string theory,however, we do not havea workable second quantized formalism. Instead, wehave to rely on a rst quantized description. The weak coupling expansion consists of histories spanning worldsheets of successively higher top ologies. Yet, the afore- mentioned divergences are still present, and are found in a sp eci c corner of mo duli space. The divergences app ear as violations of conformal invariance, as describ ed b elow. To the lowest order, these singularities are found when one consideres worldsheets as depicted in Fig. 2. P Fig. 2: The surface . P This surface, , is obtained by attaching a very long and thin strip to the b oundary of the disc. This is equivalent to removing two small segments of the b oundary of the disc and identifying them, thus creating a surface with the top ology of an annulus. In the degeneration limit, when the strip b ecomes in nitely long and thin, the only contribution comes from massless op en string states propagating along the strip. In the case of Dirichlet b oundary conditions, the only such states are the translational zero mo des. In the case of closed string solitons, the divergence app ears for degenerate surfaces containing long thin handles, along which the zero mo de, a closed string state in that 3 case, propagates. In b oth cases these limiting world-histories are reminiscent of the eld theory Feynman diagrams, as in Fig. 1 . We are now ready to prop erly extract the divergences. As discussed in [7] for the closed b osonic string theory, the matrix element in the degeneration limit can b e obtained by a conformal eld theory calculation on the lower genus surface, with op erators inserted on the degenerating segments (see Fig. 3 ). P Fig. 3: The degenerations limit of the surface . This can b e expressed formally as follows: Z X dq 2h a q h (s ) (s ) V :::V i (2.1) hV :::V i = a 1 a 2 1 n Disc 1 n q a where f g is a complete set of eigenstates of L (which generates translations along the a 0 strip), with weights h . The limit q ! 0, therefore, pro jects the sum into the lowest a weight states. As an illustration, it is useful to rst consider the same limit for the usual op en b osonic string (with Neumann b oundary conditions). The lowest weight states (excluding the tachyon) are: ! i p dX i ik X = N g e (2.2) k k ds 2 k with h = and N a normalization factor. Using the ab ove formula (2.1), one gets: k k 2 Z Z d D E X d k 2 (1+k ) i i hV :::V i = dq q (s ) (s ) V :::V : (2.3) 1 n 1 2 1 n k k d Disc (2 ) i This expression exhibits the exchange of a photon, where log q is the time parametrizing the photon worldline. The requirement of factorization xes the normalization of the op erators . a 4 Wenow turn to the analysis for the D-branes, which is rather similar. The Dirichlet N 0 p p-brane is de ned by imp osing Neumann b oundary conditions on X = X :::X , and D Dirichlet b oundary conditions on the remaining co ordinates, X . The lightest states (excluding the tachyon) are the translational zero mo des of the D-brane: D i! X 0 = N@ X e i = p +1;:::;d 1 : (2.4) i n i where X is target time, @ is the derivative normal to the b oundary, and N is a normal- 0 n ization constant. The existence of these zero mo des re ects the degeneracy of di erent ~ D-branes con gurations, obtained by rigid translations (k = 0) in the Dirichlet direc- N tions. In order to allow a general p-brane (p> 0) to recoil one needs to compactify the spatial Neumann directions and wrap the p-brane around them. In that case the mass of the p- brane is nite and prop ortional to the spatial Neumann volume. For the sake of clarity we fo cus on the scattering o a 0-brane, where no such compacti cation is necessary. The normalization constant N that app ears in (2.4) is determined by factorization; consider the S-matrix elementinvolving two closed string tachyons whose vertex op erators are: Z D D ~ ~ 2 i! X (z )ik X (z ) 1 0 1 1 1 V = N d z e 1 t 1 Z D D ~ ~ 2 i! X (z )ik X (z ) 2 0 2 2 2 V = N d z e : (2.5) 2 t 2 The factorization on op en string p oles is obtained by letting one of the tachyons approach the b oundary (see Fig. 4). Fig. 4: Factorization on the Disc. In the factorization one recognizes the various op en string p oles, in particular the 1 2 2 tachyon at ! = , and the zero mo de at ! = 0. This yields the normalization factor 2 5 1 for the zero mo de: p g : (2.6) N = 4 Since these states don't carry Dirichlet momenta, they are discrete quantum mechan- ical states. We are now ready to extract the violations of conformal invariance for S-matrix ele- ments calculated on the annulus. As mentioned ab ove, these divergences app ear in the limit of mo duli space describ ed in Fig.
Load more

Recommended publications
  • An Introduction to Effective Field Theory
    An Introduction to Effective Field Theory Thinking Effectively About Hierarchies of Scale c C.P. BURGESS i Preface It is an everyday fact of life that Nature comes to us with a variety of scales: from quarks, nuclei and atoms through planets, stars and galaxies up to the overall Universal large-scale structure. Science progresses because we can understand each of these on its own terms, and need not understand all scales at once. This is possible because of a basic fact of Nature: most of the details of small distance physics are irrelevant for the description of longer-distance phenomena. Our description of Nature’s laws use quantum field theories, which share this property that short distances mostly decouple from larger ones. E↵ective Field Theories (EFTs) are the tools developed over the years to show why it does. These tools have immense practical value: knowing which scales are important and why the rest decouple allows hierarchies of scale to be used to simplify the description of many systems. This book provides an introduction to these tools, and to emphasize their great generality illustrates them using applications from many parts of physics: relativistic and nonrelativistic; few- body and many-body. The book is broadly appropriate for an introductory graduate course, though some topics could be done in an upper-level course for advanced undergraduates. It should interest physicists interested in learning these techniques for practical purposes as well as those who enjoy the beauty of the unified picture of physics that emerges. It is to emphasize this unity that a broad selection of applications is examined, although this also means no one topic is explored in as much depth as it deserves.
    [Show full text]
  • Soft Gravitons and the Flat Space Limit of Anti-Desitter Space
    RUNHETC-2016-15, UTTG-18-16 Soft Gravitons and the Flat Space Limit of Anti-deSitter Space Tom Banks Department of Physics and NHETC Rutgers University, Piscataway, NJ 08854 E-mail: [email protected] Willy Fischler Department of Physics and Texas Cosmology Center University of Texas, Austin, TX 78712 E-mail: fi[email protected] Abstract We argue that flat space amplitudes for the process 2 n gravitons at center of mass → energies √s much less than the Planck scale, will coincide approximately with amplitudes calculated from correlators of a boundary CFT for AdS space of radius R LP , only ≫ when n < R/LP . For larger values of n in AdS space, insisting that all the incoming energy enters “the arena”[20] , implies the production of black holes, whereas there is no black hole production in the flat space amplitudes. We also argue, from unitarity, that flat space amplitudes for all n are necessary to reconstruct the complicated singularity arXiv:1611.05906v3 [hep-th] 8 Apr 2017 at zero momentum in the 2 2 amplitude, which can therefore not be reproduced as → the limit of an AdS calculation. Applying similar reasoning to amplitudes for real black hole production in flat space, we argue that unitarity of the flat space S-matrix cannot be assessed or inferred from properties of CFT correlators. 1 Introduction The study of the flat space limit of correlation functions in AdS/CFT was initiated by the work of Polchinski and Susskind[20] and continued in a host of other papers. Most of those papers agree with the contention, that the limit of Witten diagrams for CFT correlators smeared with appropriate test functions, for operators carrying vanishing angular momentum on the compact 1 space,1 converge to flat space S-matrix elements between states in Fock space.
    [Show full text]
  • King's Research Portal
    King’s Research Portal DOI: 10.1088/1742-6596/631/1/012089 Document Version Publisher's PDF, also known as Version of record Link to publication record in King's Research Portal Citation for published version (APA): Sarkar, S. (2015). String theory backgrounds with torsion in the presence of fermions and implications for leptogenesis. Journal of Physics: Conference Series, 631(1), [012089]. 10.1088/1742-6596/631/1/012089 Citing this paper Please note that where the full-text provided on King's Research Portal is the Author Accepted Manuscript or Post-Print version this may differ from the final Published version. If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. And where the final published version is provided on the Research Portal, if citing you are again advised to check the publisher's website for any subsequent corrections. General rights Copyright and moral rights for the publications made accessible in the Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognize and abide by the legal requirements associated with these rights. •Users may download and print one copy of any publication from the Research Portal for the purpose of private study or research. •You may not further distribute the material or use it for any profit-making activity or commercial gain •You may freely distribute the URL identifying the publication in the Research Portal Take down policy If you believe that this document breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim.
    [Show full text]
  • Collective Coordinates for D-Branes
    UTTG-01-96 Collective Coordinates for D-branes Willy Fischler, Sonia Paban and Moshe Rozali∗ Theory Group, Department of Physics University of Texas, Austin, Texas 78712 Abstract We develop a formalism for the scattering off D-branes that includes collective co- ordinates. This allows a systematic expansion in the string coupling constant for such processes, including a worldsheet calculation for the D-brane’s mass. 1 Introduction In the recent developments of string theory, solitons play a central role. For example, in the case of duality among various string theories, solitons of a weakly coupled string theory become elementary excitations of the dual theory [1]. Another example, among many others, is the role of solitons in resolving singularities in compactified geometries, as they become light [2]. In order to gain more insight in the various aspects of these recent developments, it is important to understand the dynamics of solitons in the context of string theory. In this quest one of the tools at our disposal is the use of scattering involving these solitons. This includes the scattering of elementary string states off these solitons as well as the arXiv:hep-th/9604014v2 11 Apr 1996 scattering among solitons. An important class of solitons that have emerged are D-branes [4]. In an influential paper [3] it was shown that these D-branes carry R R charges, − and are therefore a central ingredient in the aforementioned dualities. These objects are described by simple conformal field theories, which makes them particularly suited for explicit calculations. In this paper we use some of the preliminary ideas about collective coordinates de- veloped in a previous paper [5], to describe the scattering of elementary string states off D-branes.
    [Show full text]
  • Copyright by Juan Felipe Pedraza Avella 2015
    Copyright by Juan Felipe Pedraza Avella 2015 The Dissertation Committee for Juan Felipe Pedraza Avella certifies that this is the approved version of the following dissertation: Dynamics of asymptotically AdS spaces and holography Committee: Willy Fischler, Supervisor Jacques Distler Can Kilic Andrew Neitzke Sonia Paban Dynamics of asymptotically AdS spaces and holography by Juan Felipe Pedraza Avella, B.S., M.S. DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT AUSTIN August 2015 Dedicated to my family. Acknowledgments Many people contributed to the research presented in this thesis. I would like to start by thanking my supervisor, prof. Willy Fischler, for his excellent support and guidance over the past five years. I am also grateful to my collaborators: Cesar Ag´on,Tom Banks, Elena C´aceres,Mariano Cherni- coff, Brandon DiNunno, Mohammad Edalati, Bartomeu Fiol, Antonio Garc´ıa, Alberto G¨uijosa,Matthias Ihl, Niko Jokela, Arnab Kundu, Sandipan Kundu, Patricio Letelier,1 Fabio Lora, Phuc Nguyen, Paolo Ospina, Javier Ramos, Walter Tangarife and Di-Lun Yang. For all the time we spent discussing physics, which lead to many successful ideas [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. Finally, I would like to thank my fellow students and the professors of the UT Theory Group, for sharing their vast knowledge in individual discussions, seminars and journal club meetings. This material is based upon work supported by the National Science Foundation under Grant PHY-1316033 and by the Texas Cosmology Center, which is supported by the College of Natural Sciences, the Department of As- tronomy at the University of Texas at Austin and the McDonald Observatory.
    [Show full text]
  • Jhep11(2018)072
    Published for SISSA by Springer Received: September 12, 2018 Accepted: November 5, 2018 Published: November 12, 2018 Chaos and entanglement spreading in a non-commutative gauge theory JHEP11(2018)072 Willy Fischler,a Viktor Jahnkeb and Juan F. Pedrazac aTheory Group, Department of Physics and Texas Cosmology Center, The University of Texas at Austin, Austin, TX 78712, U.S.A. bDepartamento de F´ısica de Altas Energias, Instituto de Ciencias Nucleares, Universidad Nacional Aut´onomade M´exico, Apartado Postal 70-543, CDMX 04510, M´exico cInstitute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands E-mail: [email protected], [email protected], [email protected] Abstract: Holographic theories with classical gravity duals are maximally chaotic: they saturate a set of bounds on the spread of quantum information. In this paper we question whether non-locality can affect such bounds. Specifically, we consider the gravity dual of a prototypical theory with non-local interactions, namely, N = 4 non-commutative super Yang Mills. We construct shock waves geometries that correspond to perturbations of the thermofield double state with definite momentum and study several chaos related properties of the theory, including the butterfly velocity, the entanglement velocity, the scrambling time and the maximal Lyapunov exponent. The latter two are unaffected by the non- commutative parameter θ, however, both the butterfly and entanglement velocities increase with the strength of the non-commutativity. This implies that non-local interactions can enhance the effective light-cone for the transfer of quantum information, eluding previously conjectured bounds encountered in the context of local quantum field theory.
    [Show full text]
  • Nonperturbative Formulations of Superstring Theory
    NONPERTURBATIVE FORMULATIONS OF SUPERSTRING THEORY BY LUBOSˇ MOTL A dissertation submitted to the Graduate School—New Brunswick Rutgers, The State University of New Jersey in partial fulfillment of the requirements for the degree of Doctor of Philosophy Graduate Program in Physics and Astronomy Written under the direction of Thomas Banks and approved by arXiv:hep-th/0109149v1 19 Sep 2001 New Brunswick, New Jersey October, 2001 ABSTRACT OF THE DISSERTATION Nonperturbative Formulations of Superstring Theory by LuboˇsMotl Dissertation Director: Thomas Banks After a short introduction to Matrix theory, we explain how can one generalize matrix models to describe toroidal compactifications of M-theory and the heterotic vacua with 16 supercharges. This allows us, for the first time in history, to derive the conventional perturbative type IIA string theory known in the 80s within a complete and consistent non- perturbative framework, using the language of orbifold conformal field theory and conformal perturbation methods. A separate chapter is dedicated to the vacua with Hoˇrava-Witten domain walls that carry E8 gauge supermultiplets. Those reduce the gauge symmetry of the matrix model from U(N) to O(N). We also explain why these models contain open membranes. The compactification of M-theory on T 4 involves the so-called (2, 0) supercon- formal field theory in six dimensions, compactified on T 5. A separate chapter describes an interesting topological contribution to the low energy equations of motion on the Coulomb branch of the (2, 0) theory that admits a skyrmionic solution that we call “knitting five- branes”. Then we return to the orbifolds of Matrix theory and construct a formal classical matrix model of the Scherk-Schwarz compactification of M-theory and type IIA string theory as well as type 0 theories.
    [Show full text]
  • What Is String Theory?
    hep-th/yymmnn SCIPP-2010/04 What is String Theory? Tom Banks and Michael Dine Santa Cruz Institute for Particle Physics and Department of Physics, University of California, Santa Cruz CA 95064 Abstract We describe, for a general audience, the current state of string theory. We explain that nature is almost certainly not described by string theory as we know it, but that string theory does show us that quantum mechanics and gravity can coexist, and points to the possible theory of quantum gravity which describes the world around us. Directions for research, both on the nature of this theory and its predictions, are described. 1 Introduction Over the past three decades, high energy physicists have developed an exquisite understanding of the laws of nature, governing phenomena down to distances scales as small as 10-17 cm. This Standard Model has proven so successful as to be, at some level, a source of frustration. There are many questions that we would like to understand, for which the Standard Model does not provide satisfying explanations. Some of these - what is the origin of the mass of the electron, quarks, and other particles, why is gravity so much weaker than the other forces, what is the nature of the dark matter - may be answered at the Large Hadron Collider, which, after some setbacks, is beginning operation in Geneva, Switzerland. Others require new theoretical structures. Perhaps the 1.Introduction. Over the past three decades, high energy physicists have developed an exquisite understanding of the laws of nature, governing phenomena down to distances scales as small as 10-17 cm.
    [Show full text]
  • Arxiv:Hep-Th/0303076 V1 9 Mar 2003
    hep-th/0303076 SCIPP-2003/09 MIFP-03-04 PUPT-2075 Closed String Tachyons and Their Implications for Non-Supersymmetric Strings Michael Dine and Elie Gorbatov Santa Cruz Institute for Particle Physics, Santa Cruz CA 95064 Igor R. Klebanov1 School of Natural Science, Institute for Advanced Study, Princeton, NJ 08540 and George P. & Cynthia W. Mitchell Institute for Fundamental Physics Texas A& M University, College Station, TX 77843 Michael Krasnitz Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 Abstract arXiv:hep-th/0303076 v1 9 Mar 2003 Closed string tachyons have long been somewhat mysterious. We note that there is often a regime in the classical moduli space in which one can systematically compute the effective action for such fields. In this regime, the tachyon is light, and cannot be integrated out. Instead, one must consider the combined dynamics of gravitons, moduli, tachyons and other light fields. We compute the action and find that the quartic term for the tachyon is positive in the field definition where the tachyon has no derivative coupling to the radion. We study the evolution of isotropic, homogeneous configurations and find that typically the system is driven to regions where the calculation is no longer under control. 1On leave from Princeton University, Princeton, NJ 08544 1 Introduction Most known non-supersymmetric string theories contain tachyons. For years there seemed to be no reliable technique in string theory to compute the potential for tachyonic fields (nor was it clear that such a potential is meaningful), and so it was hard to tell whether they are similar to familiar sorts of field theory instabilities, or represent some new phenomena.
    [Show full text]
  • Copyright by Chethan Krishnan 2006 the Dissertation Committee for Chethan Krishnan Certifies That This Is the Approved Version of the Following Dissertation
    Copyright by Chethan Krishnan 2006 The Dissertation Committee for Chethan Krishnan certifies that this is the approved version of the following dissertation: Aspects of Cosmology and Quantum Gravity in an Accelerating Universe Committee: Willy Fischler, Supervisor Jacques Distler Sonia Paban Steven Weinberg Lorenzo Sadun Aspects of Cosmology and Quantum Gravity in an Accelerating Universe by Chethan Krishnan, B.Tech. DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT AUSTIN August 2006 Acknowledgments I was extremely fortunate to have Willy as my adviser, and I wish to thank him here for that. His way of focusing on what is ultimately important as opposed to what is cosmetic, has made a crucial impact on my thinking. Doing physics with him and Sonia was an entertaining and enlightening ex- perience. My “theory friends” -Marija, Jeff, Uday, Aron, Marcus, Steve, the Germans, the Italians- need to be mentioned for the many interesting con- versations and also for tolerating my loudness. I would also like to thank Hyuk-Jae, who taught me a lot in my beginning years. It is a tribute to hu- man sociology that people far less capable than him seem to be able to stay on as “string theorists”. Finally, I want to thank Jan Duffy for being a paragon of patience and affection, despite my relentless efforts to test her by missing the registration deadline year after year. There were some other major influences in my life outside of RLM in these last few years.
    [Show full text]
  • CURRICULUM VITAE SONIA PABAN Address
    CURRICULUM VITAE SONIA PABAN Address: Department of Physics University of Texas at Austin Austin, TX 78712-1081 Phone: (512) 794-8010 (Home) (512) 471-7773 (Work) E-mail: [email protected] EDUCATION 1988 Ph.D., Universitat de Barcelona, Spain (Advisor: Rolf Tarrach) 1985 M.A., Universitat de Barcelona, Spain (Advisor: Pere Pascual) 1984 B.S., Universitat de Barcelona, Spain PROFESSIONAL EXPERIENCE Spring 2015 Member, Institute for Advanced Study, Princeton Fall 2014 Visiting Researcher, Center for Theoretical Physics, MIT 2006{ Associate Professor, University of Texas at Austin 2000{2006 Assistant Professor, University of Texas at Austin 1999{2000 Research Associate, University of Texas at Austin 1998{1999 Postdoc, University of Texas at Austin 1996{1998 Member, Institute for Advanced Study, Princeton Et´e'95,´ '99 Visitor, Institut des Hautes Etudes Scientifiques 1994{1996 Postdoc, University of Texas at Austin 1992{1994 Postdoc, University of Minnesota at Minneapolis 1991{1992 Postdoc, University of Texas at Austin HONORS 2014{2015 Simons Fellow in Physics 2013 University of Texas Regents' Outstanding Teaching Award 2005 College of Natural Sciences Teaching Excellence Award FELLOWSHIPS AND GRANTS 8/15- National Science Foundation 9/05{8/13 National Science Foundation 9/99{8/01 POWRE grant, National Science Foundation 9/89{8/91 Fulbright Fellowship, University of Texas at Austin 9/84{8/89 Predoctoral Grant, Spanish Government PROFESSIONAL SERVICE 2014{ Member, STEM task force, Hispanic Association of Colleges and Universities 2013{
    [Show full text]
  • Jhep01(2014)137
    Published for SISSA by Springer Received: August 2, 2013 Revised: December 6, 2013 Accepted: January 7, 2014 Published: January 24, 2014 Holographic entanglement in a noncommutative JHEP01(2014)137 gauge theory Willy Fischler,a,b Arnab Kundua and Sandipan Kundua,b aTheory Group, Department of Physics, University of Texas, Austin, TX 78712, U.S.A. bTexas Cosmology Center, University of Texas, Austin, TX 78712, U.S.A. E-mail: [email protected], [email protected], [email protected] Abstract: In this article we investigate aspects of entanglement entropy and mutual in- formation in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescrip- tion, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties. Keywords: Gauge-gravity correspondence, AdS-CFT Correspondence, Non-Commutative Geometry, Classical Theories of Gravity ArXiv ePrint: 1307.2932 Open Access, c The Authors.
    [Show full text]