On Facts in Superstring Theory
Total Page:16
File Type:pdf, Size:1020Kb

Load more
Recommended publications
-
Magnetic Vortices in Gauge/Gravity Duality
Magnetic Vortices in Gauge/Gravity Duality Dissertation by Migael Strydom Magnetic Vortices in Gauge/Gravity Duality Dissertation an der Fakult¨atf¨urPhysik der Ludwig{Maximilians{Universit¨at M¨unchen vorgelegt von Migael Strydom aus Pretoria M¨unchen, den 20. Mai 2014 Dissertation submitted to the faculty of physics of the Ludwig{Maximilians{Universit¨atM¨unchen by Migael Strydom supervised by Prof. Dr. Johanna Karen Erdmenger Max-Planck-Institut f¨urPhysik, M¨unchen 1st Referee: Prof. Dr. Johanna Karen Erdmenger 2nd Referee: Prof. Dr. Dieter L¨ust Date of submission: 20 May 2014 Date of oral examination: 18 July 2014 Zusammenfassung Wir untersuchen stark gekoppelte Ph¨anomene unter Verwendung der Dualit¨at zwischen Eich- und Gravitationstheorien. Dabei liegt ein besonderer Fokus einer- seits auf Vortex L¨osungen, die von einem magnetischem Feld verursacht werden, und andererseits auf zeitabh¨angigen Problemen in holographischen Modellen. Das wichtigste Ergebnis ist die Entdeckung eines unerwarteten Effektes in einem ein- fachen holografischen Modell: ein starkes nicht abelsches magnetisches Feld verur- sacht die Entstehung eines Grundzustandes in der Form eines dreieckigen Gitters von Vortices. Die Dualit¨at zwischen Eich- und Gravitationstheorien ist ein m¨achtiges Werk- zeug welches bereits verwendet wurde um stark gekoppelte Systeme vom Quark- Gluonen Plasma in Teilchenbeschleunigern bis hin zu Festk¨orpertheorien zu be- schreiben. Die wichtigste Idee ist dabei die der Dualit¨at: Eine stark gekoppelte Quantenfeldtheorie kann untersucht werden, indem man die Eigenschaften eines aus den Einsteinschen Feldgleichungen folgenden Gravitations-Hintergrundes be- stimmt. Eine der Gravitationstheorien, die in dieser Arbeit behandelt werden, ist ei- ne Einstein{Yang{Mills Theorie in einem AdS{Schwarzschild Hintergrund mit SU(2)-Eichsymmetrie. -
Supersymmetry Breaking from a Calabi-Yau Singularity
hep-th/0505029 NSF-KITP-05-27 Supersymmetry Breaking from a Calabi-Yau Singularity D. Berenstein∗, C. P. Herzog†, P. Ouyang∗, and S. Pinansky∗ † Kavli Institute for Theoretical Physics ∗ Physics Department University of California University of California Santa Barbara, CA 93106, USA Santa Barbara, CA 93106, USA Abstract We conjecture a geometric criterion for determining whether supersymmetry is spon- taneously broken in certain string backgrounds. These backgrounds contain wrapped branes at Calabi-Yau singularites with obstructions to deformation of the complex structure. We motivate our conjecture with a particular example: the Y 2,1 quiver gauge theory corresponding to a cone over the first del Pezzo surface, dP1. This setup can be analyzed using ordinary supersymmetric field theory methods, where we find that gaugino condensation drives a deformation of the chiral ring which has no solu- tions. We expect this breaking to be a general feature of any theory of branes at a singularity with a smaller number of possible deformations than independent anomaly- arXiv:hep-th/0505029v2 7 May 2005 free fractional branes. May 2005 1 Introduction Supersymmetry and supersymmetry breaking are central ideas both in contemporary par- ticle physics and in mathematical physics. In this paper, we argue that for a large new class of D-brane models there exists a simple geometric criterion which determines whether supersymmetry breaking occurs. The models of interest are based on Calabi-Yau singularities with D-branes placed at or near the singularity. By taking a large volume limit, it is possible to decouple gravity from the theory, and ignore the Calabi-Yau geometry far from the branes. -
Localization of Gauge Theories on the Three-Sphere
Localization of Gauge Theories on the Three-Sphere Thesis by Itamar Yaakov In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2012 (Defended May 14, 2012) ii c 2012 Itamar Yaakov All Rights Reserved iii Acknowledgements I would like to thank my research adviser, Professor Anton Kapustin, for his continuing support. His mentorship, foresight, intuition and collaboration were the keys to my having a successful graduate career. The work described here was done in collaboration with Brian Willett and much of the credit for successful completion of this work is duly his. I would also like to express my deep appreciation to the California Institute of Technology, and especially the professors and staff of the physics department for a thoroughly enjoyable and interesting five years of study. Special thanks to Frank Porter, Donna Driscoll, Virginio Sannibale, and Carol Silberstein. I am grateful to Mark Wise, John Schwarz, Hirosi Ooguri, and Frank Porter for serving on my candidacy and defense committees. I benefited from discussions along the way with Ofer Aharony, John Schwarz, Sergei Gukov, Hirosi Ooguri, David Kutasov, Zohar Komargodski, Daniel Jafferis, and Jaume Gomis. I would like to thank the organizers and lecturers of the PITP 2010 summer school at the Institute for Advanced study for an impeccably produced learning experience. My thanks also to Gregory Moore and Nathan Seiberg for taking the time to discuss my research while at the school. I would like to thank UCLA, especially Yu-tin Huang, and the Perimeter Institute and Jaume Gomis for allowing me to present my work there. -
Ads Description of Induced Higher Spin Gauge Theories
UV Completion of Some UV Fixed Points Igor Klebanov Talk at ERG2016 Conference ICTP, Trieste September 23, 2016 Talk mostly based on • L. Fei, S. Giombi, IK, arXiv:1404.1094 • S. Giombi, IK, arXiv:1409.1937 • L. Fei, S. Giombi, IK, G. Tarnopolsky, arXiv:1411.1099 • L. Fei, S. Giombi, IK, G. Tarnopolsky, arXiv:1507.01960 • L. Fei, S. Giombi, IK, G. Tarnopolsky, arXiv:1607.05316 The Gross-Neveu Model • In 2 dimensions it has some similarities with the 4-dimensional QCD. • It is asymptotically free and exhibits dynamical mass generation. • Similar physics in the 2-d O(N) non-linear sigma model with N>2. • In dimensions slightly above 2 both the O(N) and GN models have weakly coupled UV fixed points. 2+ e expansion • The beta function and fixed-point coupling are • is the number of 2-component Majorana fermions. • Can develop 2+e expansions for operator scaling dimensions, e.g. Gracey; Kivel, Stepanenko, Vasiliev • Similar expansions in the O(N) sigma model with N>2. Brezin, Zinn-Justin 4-e expansion • The O(N) sigma model is in the same universality class as the O(N) model: • It has a weakly coupled Wilson-Fisher IR fixed point in 4-e dimensions. • Using the two e expansions, the scalar CFTs with various N may be studied in the range 2<d<4. This is an excellent practical tool for CFTs in d=3. The Gross-Neveu-Yukawa Model • The GNY model is the UV completion of the GN model in d<4 Zinn-Justin; Hasenfratz, Hasenfratz, Jansen, Kuti, Shen • IR stable fixed point in 4-e dimensions • Operator scaling dimensions • Using the two e expansions, we can study the Gross-Neveu CFTs in the range 2<d<4. -
Annual Rpt 2004 For
I N S T I T U T E for A D V A N C E D S T U D Y ________________________ R E P O R T F O R T H E A C A D E M I C Y E A R 2 0 0 3 – 2 0 0 4 EINSTEIN DRIVE PRINCETON · NEW JERSEY · 08540-0631 609-734-8000 609-924-8399 (Fax) www.ias.edu Extract from the letter addressed by the Institute’s Founders, Louis Bamberger and Mrs. Felix Fuld, to the Board of Trustees, dated June 4, 1930. Newark, New Jersey. It is fundamental in our purpose, and our express desire, that in the appointments to the staff and faculty, as well as in the admission of workers and students, no account shall be taken, directly or indirectly, of race, religion, or sex. We feel strongly that the spirit characteristic of America at its noblest, above all the pursuit of higher learning, cannot admit of any conditions as to personnel other than those designed to promote the objects for which this institution is established, and particularly with no regard whatever to accidents of race, creed, or sex. TABLE OF CONTENTS 4·BACKGROUND AND PURPOSE 7·FOUNDERS, TRUSTEES AND OFFICERS OF THE BOARD AND OF THE CORPORATION 10 · ADMINISTRATION 12 · PRESENT AND PAST DIRECTORS AND FACULTY 15 · REPORT OF THE CHAIRMAN 20 · REPORT OF THE DIRECTOR 24 · OFFICE OF THE DIRECTOR - RECORD OF EVENTS 31 · ACKNOWLEDGMENTS 43 · REPORT OF THE SCHOOL OF HISTORICAL STUDIES 61 · REPORT OF THE SCHOOL OF MATHEMATICS 81 · REPORT OF THE SCHOOL OF NATURAL SCIENCES 107 · REPORT OF THE SCHOOL OF SOCIAL SCIENCE 119 · REPORT OF THE SPECIAL PROGRAMS 139 · REPORT OF THE INSTITUTE LIBRARIES 143 · INDEPENDENT AUDITORS’ REPORT 3 INSTITUTE FOR ADVANCED STUDY BACKGROUND AND PURPOSE The Institute for Advanced Study was founded in 1930 with a major gift from New Jer- sey businessman and philanthropist Louis Bamberger and his sister, Mrs. -
Studies in Field Theories: Mhv Vertices, Twistor Space, Recursion Relations and Chiral Rings
STUDIES IN FIELD THEORIES: MHV VERTICES, TWISTOR SPACE, RECURSION RELATIONS AND CHIRAL RINGS Peter Svr·cek Advisor: Edward Witten A DISSERTATION SUBMITTED TO THE FACULTY OF PRINCETON UNIVERSITY IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY RECOMMENDED FOR ACCEPTANCE BY THE DEPARTMENT OF PHYSICS April 2005 Copyright °c 2005 by Peter Svr·cek All rights reserved. ii Abstract In this thesis we study di®erent aspects of four dimensional ¯eld theories. In the ¯rst chapter we give introduction and overview of the thesis. In the second chapter we review the connection between perturbative Yang-Mills and twistor string the- ory. Inspired by this, we propose a new way of constructing Yang-Mills scattering amplitudes from Feynman graphs in which the vertices are o®-shell continuations of the tree level MHV amplitudes. The MHV diagrams lead to simple formulas for tree-level amplitudes. We then give a heuristic derivation of the diagrams from twistor string theory. In the third chapter, we explore the twistor structure of scattering amplitudes in theories for which a twistor string theory analogous to the one for N = 4 gauge theory has not yet been proposed. We study the di®erential equations of one-loop amplitudes of gluons in gauge theories with reduced supersymmetry and of tree level and one-loop amplitudes of gravitons in general relativity and supergravity. We ¯nd that the scattering amplitudes localize in twistor space on algebraic curves that are surprisingly similar to the N = 4 Yang-Mills case. In the next chapter we propose tree-level recursion relations for scattering am- plitudes of gravitons. -
Supersymmetric Dualities and Quantum Entanglement in Conformal Field Theory
Supersymmetric Dualities and Quantum Entanglement in Conformal Field Theory Jeongseog Lee A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy Recommended for Acceptance by the Department of Physics Adviser: Igor R. Klebanov September 2016 c Copyright by Jeongseog Lee, 2016. All rights reserved. Abstract Conformal field theory (CFT) has been under intensive study for many years. The scale invariance, which arises at the fixed points of renormalization group in rela- tivistic quantum field theory (QFT), is believed to be enhanced to the full conformal group. In this dissertation we use two tools to shed light on the behavior of certain conformal field theories, the supersymmetric localization and the quantum entangle- ment Renyi entropies. The first half of the dissertation surveys the infrared (IR) structure of the = 2 N supersymmetric quantum chromodynamics (SQCD) in three dimensions. The re- cently developed F -maximization principle shows that there are richer structures along conformal fixed points compared to those in = 1 SQCD in four dimensions. N We refer to one of the new phenomena as a \crack in the conformal window". Using the known IR dualities, we investigate it for all types of simple gauge groups. We see different decoupling behaviors of operators depending on the gauge group. We also observe that gauging some flavor symmetries modifies the behavior of the theory in the IR. The second half of the dissertation uses the R`enyi entropy to understand the CFT from another angle. At the conformal fixed points of even dimensional QFT, the entanglement entropy is known to have the log-divergent universal term depending on the geometric invariants on the entangling surface. -
Gravity, Gauge Theory and Strings
Les Houches - Ecole d'Ete de Physique Theorique 76 Unity from Duality: Gravity, Gauge Theory and Strings Les Houches Session LXXVI, July 30 - August 31, 2001 Bearbeitet von Constantin P. Bachas, Adel Bilal, Michael R. Douglas, Nikita A. Nekrasov, Francois David 1. Auflage 2003. Buch. xxxiv, 664 S. Hardcover ISBN 978 3 540 00276 5 Format (B x L): 15,5 x 23,5 cm Gewicht: 1220 g Weitere Fachgebiete > Technik > Verfahrenstechnik, Chemieingenieurwesen, Lebensmitteltechnik Zu Inhaltsverzeichnis schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, eBooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte. Preface The 76th session of the Les Houches Summer School in Theoretical Physics was devoted to recent developments in string theory, gauge theories and quantum gravity. As frequently stated, Superstring Theory is the leading candidate for a unified theory of all fundamental physical forces and elementary parti- cles. This claim, and the wish to reconcile general relativity and quantum mechanics, have provided the main impetus for the development of the the- ory over the past two decades. More recently the discovery of dualities, and of important new tools such as D-branes, has greatly reinforced this point of view. On the one hand there is now good reason to believe that the underlying theory is unique. On the other hand, we have for the first time working (though unrealistic) microscopic models of black hole mechan- ics. -
Arxiv:Hep-Th/9809022V2 8 Sep 1998
NSF-ITP-98-086 hep-th/9809022 UV/IR Relations in AdS Dynamics Amanda W. Peet1 and Joseph Polchinski2 Institute for Theoretical Physics University of California Santa Barbara, CA 93106-4030 Abstract We point out that two distinct distance–energy relations have been discussed in the AdS/CFT correspondence. In conformal backgrounds they differ only in normalization, but in nonconformal backgrounds they differ in functional form. We discuss the relation to probe pro- cesses, the holographic principle, and black hole entropies. arXiv:hep-th/9809022v2 8 Sep 1998 [email protected] [email protected] 1 An important feature of the recently discovered AdS/CFT duality is a correspondence between long distances in the AdS space and high energies in the CFT [1, 2]. In fact, at least two quite distinct distance–energy rela- tions have been discussed. While this point may have been noted implicitly elsewhere, we believe that it is instructive to discuss it in some detail. In sec- tion 1 we consider various conformally invariant spaces (D3, M5, and M2). In section 2 we consider conformally noninvariant Dp-brane spaces, where new issues arise. 1 Conformal theories 1.1 The D3-brane For illustration let us consider the near-horizon geometry of N D3-branes, the AdS5 × S5 space with string metric 2 1/2 2 ′ U 2 gYMN 2 2 2 ds = α 1/2 dxk + 2 (dU + U dΩ5) (1.1) "gYMN U # Φ 2 and a constant dilaton e = gs = gYM. We use the conventions of refs. [1, 3] but omit all numerical constants. -
Positive Geometry of the S-Matrix
Positive Geometry of the S-Matrix Yuntao Bai A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy Recommended for Acceptance by the Department of Physics Adviser: Nima Arkani-Hamed September 2018 © Copyright by Yuntao Bai, 2018. All rights reserved. Abstract The search for a theory of the S-Matrix has revealed unprecedented structures under- lying amplitudes. In this text, we present a new framework for understanding a class of amplitudes that includes Yang-Mills, Non-linear Sigma Model, the bi-adjoint cubic scalar, planar N = 4 super Yang-Mills, and more. We introduce positive geometries, which are generalizations of convex polytopes to geometries with higher order (i.e. non-linear) boundaries. Our construction provides a unique differential form called the canonical form of the positive geometry, whose pole structure is completely con- trolled by the geometric boundaries. The central claim of this text is that positive geometries play a fundamental role in our class of scattering amplitudes, whereby the corresponding canonical form determines a physical quantity. Our primary examples are (1) the bi-adjoint cubic scalar for which the positive geometry is the famous as- sociahedron polytope whose canonical form gives the color-ordered tree amplitude, and (2) planar N = 4 super Yang-Mills for which the positive geometry is the ampli- tuhedron whose canonical form gives the scattering integrand. One recurrent theme in our text is that physical properties of amplitudes like local poles and factorization are direct consequences of the boundary structure. We are therefore led to the point of view that locality and unitarity are emergent properties of the positive geometry. -
Theoretical Studies of Cosmic Acceleration
University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2016 Theoretical Studies of Cosmic Acceleration James Stokes University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Physics Commons Recommended Citation Stokes, James, "Theoretical Studies of Cosmic Acceleration" (2016). Publicly Accessible Penn Dissertations. 2040. https://repository.upenn.edu/edissertations/2040 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/2040 For more information, please contact [email protected]. Theoretical Studies of Cosmic Acceleration Abstract In this thesis we describe theoretical approaches to the problem of cosmic acceleration in the early and late universe. The first approach we consider relies upon the modification of Einstein gravity by the inclusion of mass terms as well as couplings to higher-derivative scalar fields possessing generalized internal shift symmetries - the Galileons. The second half of the thesis is concerned with the quantum- mechanical consistency of a theory of the early universe known as the pseudo-conformal mechanism which, in contrast to inflation, eliesr not on the effects of gravity but on conformal field theory (CFT) dynamics. It is possible to couple Dirac-Born-Infeld (DBI) scalars possessing generalized Galilean internal shift symmetries (Galileons) to nonlinear massive gravity in four dimensions, in such a manner that the interactions maintain the Galilean symmetry. Such a construction is of interest because it is not possible to couple such fields ot massless General Relativity in the same way. Using tetrad techniques we show that this massive gravity-Galileon theory possesses a primary constraint necessary to ensure propagation with the correct number of degrees of freedom. -
O(N) Models with Boundary Interactions and Their Long Range Generalizations
PUPT-2606 O(N) Models with Boundary Interactions and their Long Range Generalizations Simone Giombi1 and Himanshu Khanchandani1 1Department of Physics, Princeton University, Princeton, NJ 08544, USA Abstract We study the critical properties of scalar field theories in d + 1 dimensions with O(N) invariant interactions localized on a d-dimensional boundary. By a combination of large N and epsilon expansions, we provide evidence for the existence of non-trivial O(N) BCFTs in 1 < d < 4. Due to having free fields in the bulk, these models possess bulk higher-spin currents which are conserved up to terms localized on the boundary. We suggest that this should lead to a set of protected spinning operators on the boundary, and give evidence that arXiv:1912.08169v3 [hep-th] 14 Sep 2020 their anomalous dimensions vanish. We also discuss the closely related long-range O(N) models in d dimensions, and in particular study a weakly coupled description of the d = 1 long range O(N) model near the upper critical value of the long range parameter, which is given in terms of a non-local non-linear sigma model. By combining the known perturbative descriptions, we provide some estimates of critical exponents in d = 1. September 15, 2020 Contents 1 Introduction and Summary2 2 Free fields with boundary interactions: some general remarks7 2.1 Displacement operator and its higher spin cousins . 11 3 O(N) BCFT in 1 < d < 4 13 3.1 φ4 theory in d = 2 − .............................. 13 3.2 Large N description for general d ........................ 19 3.3 Non-linear sigma model in d = 1 + ......................