Shamit Kachru Professor of Physics and Director, Stanford Institute for Theoretical Physics
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Quantum Symmetries and Stringy Instantons
PUPT–1464 hep-th@xxx/9406091 Quantum Symmetries and Stringy Instantons ⋆ Jacques Distler and Shamit Kachru† Joseph Henry Laboratories Princeton University Princeton, NJ 08544 USA The quantum symmetry of many Landau-Ginzburg orbifolds appears to be broken by Yang-Mills instantons. However, isolated Yang-Mills instantons are not solutions of string theory: They must be accompanied by gauge anti-instantons, gravitational instantons, or topologically non-trivial configurations of the H field. We check that the configura- tions permitted in string theory do in fact preserve the quantum symmetry, as a result of non-trivial cancellations between symmetry breaking effects due to the various types arXiv:hep-th/9406091v1 14 Jun 1994 of instantons. These cancellations indicate new constraints on Landau-Ginzburg orbifold spectra and require that the dilaton modulus mix with the twisted moduli in some Landau- Ginzburg compactifications. We point out that one can find similar constraints at all fixed points of the modular group of the moduli space of vacua. June 1994 †Address after June 30: Department of Physics, Harvard University, Cambridge, MA 02138. ⋆ Email: [email protected], [email protected] . Research supported by NSF grant PHY90-21984, and the A. P. Sloan Foundation. 1. Introduction Landau-Ginzburg orbifolds [1,2] describe special submanifolds in the moduli spaces of Calabi-Yau models, at “very small radius.” New, stringy features of the physics are therefore often apparent in the Landau-Ginzburg theories. For example, these theories sometimes manifest enhanced gauge symmetries which do not occur in the field theory limit, where the large radius manifold description is valid. -
Inflation in String Theory: - Towards Inflation in String Theory - on D3-Brane Potentials in Compactifications with Fluxes and Wrapped D-Branes
1935-6 Spring School on Superstring Theory and Related Topics 27 March - 4 April, 2008 Inflation in String Theory: - Towards Inflation in String Theory - On D3-brane Potentials in Compactifications with Fluxes and Wrapped D-branes Liam McAllister Department of Physics, Stanford University, Stanford, CA 94305, USA hep-th/0308055 SLAC-PUB-9669 SU-ITP-03/18 TIFR/TH/03-06 Towards Inflation in String Theory Shamit Kachru,a,b Renata Kallosh,a Andrei Linde,a Juan Maldacena,c Liam McAllister,a and Sandip P. Trivedid a Department of Physics, Stanford University, Stanford, CA 94305, USA b SLAC, Stanford University, Stanford, CA 94309, USA c Institute for Advanced Study, Princeton, NJ 08540, USA d Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, INDIA We investigate the embedding of brane inflation into stable compactifications of string theory. At first sight a warped compactification geometry seems to produce a naturally flat inflaton potential, evading one well-known difficulty of brane-antibrane scenarios. Care- arXiv:hep-th/0308055v2 23 Sep 2003 ful consideration of the closed string moduli reveals a further obstacle: superpotential stabilization of the compactification volume typically modifies the inflaton potential and renders it too steep for inflation. We discuss the non-generic conditions under which this problem does not arise. We conclude that brane inflation models can only work if restric- tive assumptions about the method of volume stabilization, the warping of the internal space, and the source of inflationary energy are satisfied. We argue that this may not be a real problem, given the large range of available fluxes and background geometries in string theory. -
Some Comments on Equivariant Gromov-Witten Theory and 3D Gravity (A Talk in Two Parts) This Theory Has Appeared in Various Interesting Contexts
Some comments on equivariant Gromov-Witten theory and 3d gravity (a talk in two parts) This theory has appeared in various interesting contexts. For instance, it is a candidate dual to (chiral?) supergravity with deep negative cosmologicalShamit constant. Kachru Witten (Stanford & SLAC) Sunday, April 12, 15 Tuesday, August 11, 15 Much of the talk will be review of things well known to various parts of the audience. To the extent anything very new appears, it is based on two recent collaborative papers: * arXiv : 1507.00004 with Benjamin, Dyer, Fitzpatrick * arXiv : 1508.02047 with Cheng, Duncan, Harrison Some slightly older work with other (also wonderful) collaborators makes brief appearances. Tuesday, August 11, 15 Today, I’d like to talk about two distinct topics. Each is related to the general subjects of this symposium, but neither has been central to any of the talks we’ve heard yet. 1. Extremal CFTs and quantum gravity ...where we see how special chiral CFTs with sparse spectrum may be important in gravity... II. Equivariant Gromov-Witten & K3 ...where we see how certain enumerative invariants of K3 may be related to subjects we’ve heard about... Tuesday, August 11, 15 I. Extremal CFTs and quantum gravity A fundamental role in our understanding of quantum gravity is played by the holographic correspondence between conformal field theories and AdS gravity. In the basic dictionary between these subjects conformal symmetry AdS isometries $ primary field of dimension ∆ bulk quantum field of mass m(∆) $ ...... Tuesday, August 11, 15 -
Is String Theory Holographic? 1 Introduction
Holography and large-N Dualities Is String Theory Holographic? Lukas Hahn 1 Introduction1 2 Classical Strings and Black Holes2 3 The Strominger-Vafa Construction3 3.1 AdS/CFT for the D1/D5 System......................3 3.2 The Instanton Moduli Space.........................6 3.3 The Elliptic Genus.............................. 10 1 Introduction The holographic principle [1] is based on the idea that there is a limit on information content of spacetime regions. For a given volume V bounded by an area A, the state of maximal entropy corresponds to the largest black hole that can fit inside V . This entropy bound is specified by the Bekenstein-Hawking entropy A S ≤ S = (1.1) BH 4G and the goings-on in the relevant spacetime region are encoded on "holographic screens". The aim of these notes is to discuss one of the many aspects of the question in the title, namely: "Is this feature of the holographic principle realized in string theory (and if so, how)?". In order to adress this question we start with an heuristic account of how string like objects are related to black holes and how to compare their entropies. This second section is exclusively based on [2] and will lead to a key insight, the need to consider BPS states, which allows for a more precise treatment. The most fully understood example is 1 a bound state of D-branes that appeared in the original article on the topic [3]. The third section is an attempt to review this construction from a point of view that highlights the role of AdS/CFT [4,5]. -
Non-Higgsable Clusters for 4D F-Theory Models
Non-Higgsable clusters for 4D F-theory models The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Morrison, David R., and Washington Taylor. “Non-Higgsable Clusters for 4D F-Theory Models.” J. High Energ. Phys. 2015, no. 5 (May 2015). As Published http://dx.doi.org/10.1007/jhep05(2015)080 Publisher Springer-Verlag Version Final published version Citable link http://hdl.handle.net/1721.1/98237 Terms of Use Creative Commons Attribution Detailed Terms http://creativecommons.org/licenses/by/4.0/ Published for SISSA by Springer Received: January 6, 2015 Accepted: April 18, 2015 Published: May 18, 2015 Non-Higgsable clusters for 4D F-theory models JHEP05(2015)080 David R. Morrisona and Washington Taylorb aDepartments of Mathematics and Physics, University of California, Santa Barbara, Santa Barbara, CA 93106, U.S.A. bCenter for Theoretical Physics, Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, U.S.A. E-mail: [email protected], [email protected] Abstract: We analyze non-Higgsable clusters of gauge groups and matter that can arise at the level of geometry in 4D F-theory models. Non-Higgsable clusters seem to be generic features of F-theory compactifications, and give rise naturally to structures that include the nonabelian part of the standard model gauge group and certain specific types of potential dark matter candidates. In particular, there are nine distinct single nonabelian gauge group factors, and only five distinct products of two nonabelian gauge group factors with matter, including SU(3) × SU(2), that can be realized through 4D non-Higgsable clusters. -
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Arxiv:1808.09134V2 [Hep-Th] 24 Sep 2018
KIAS-P18089 Algebraic surfaces, Four-folds and Moonshine Kimyeong Lee1, ∗ and Matthieu Sarkis1, y 1School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea The aim of this note is to point out an interesting fact related to the elliptic genus of complex algebraic surfaces in the context of Mathieu moonshine. We also discuss the case of 4-folds. INTRODUCTION terms of the holomorphic Euler characteristic of a for- mal series with holomorphic vector bundle coefficients. In their seminal paper [1], Eguchi, Ooguri and We give for it a simple expression in terms the self- Tachikawa made the interesting observation that the el- intersection number of the canonical class and the Euler liptic genus of K3 admits a decomposition in terms of number. One can then deduce the behaviour of the ellip- N = 4 super-Virasoro characters, whose coefficients hap- tic genus under blow ups, allowing us to state in which 2 pen to correspond to the dimension of representations sense any surface with positive K may be relevant for a geometric understanding of Mathieu moonshine. of the largest Mathieu sporadic group M24. This phe- nomenon was formalized in a precise conjecture related We finally discuss how the discussion for surfaces can be extended for 4-folds. to the existence of a graded module for M24 whose prop- erties would precisely mimic the experimental observa- tion of [1]. This conjecture was then proved by Gan- Conventions: non [2]. Many authors have made important contribu- • We will omit the modular argument and denote tions towards understanding Mathieu moonshine from by θ(z) the odd Jacobi theta function θ(τ; z) when a physics perspective in terms of the BPS spectrum of unambiguous, cf. -
(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. -
Vacua with Small Flux Superpotential
Vacua with Small Flux Superpotential Mehmet Demirtas,∗ Manki Kim,y Liam McAllister,z and Jakob Moritzx Department of Physics, Cornell University, Ithaca, NY 14853, USA (Dated: February 4, 2020) We describe a method for finding flux vacua of type IIB string theory in which the Gukov-Vafa- −8 Witten superpotential is exponentially small. We present an example with W0 ≈ 2 × 10 on an orientifold of a Calabi-Yau hypersurface with (h1;1; h2;1) = (2; 272), at large complex structure and weak string coupling. 1. INTRODUCTION In x2 we present a general method for constructing vacua with small W0 at large complex structure (LCS) To understand the nature of dark energy in quantum and weak string coupling, building on [9, 10]. In x3 we 1 −8 gravity, one can study de Sitter solutions of string theory. give an explicit example where W0 ≈ 2 × 10 , in an Kachru, Kallosh, Linde, and Trivedi (KKLT) have ar- orientifold of a Calabi-Yau hypersurface in CP[1;1;1;6;9]. gued that there exist de Sitter vacua in compactifications In x4 we show that our result accords well with the sta- on Calabi-Yau (CY) orientifolds of type IIB string theory tistical predictions of [4]. We show in x5 that at least one [1]. An essential component of the KKLT scenario is a complex structure modulus in our example is as light as small vacuum value of the classical Gukov-Vafa-Witten the K¨ahlermoduli. We explain why this feature occurs in [2] flux superpotential, our class of solutions, and we comment on K¨ahlermoduli stabilization in our vacuum. -
Hawking Radiation and Black Hole Thermodynamics
HAWKING RADIATION AND BLACK HOLE THERMODYNAMICS ∗ Don N. Page † Institute for Theoretical Physics Department of Physics, University of Alberta Edmonton, Alberta, Canada T6G 2J1 (2004 September 3; additional section added 2004 December 31 ‡) Abstract An inexhaustive review of Hawking radiation and black hole thermody- namics is given, focusing especially upon some of the historical aspects as seen from the biased viewpoint of a minor player in the field on and off for the past thirty years. arXiv:hep-th/0409024v3 31 Dec 2004 ∗Alberta-Thy-18-04, hep-th/0409024, review article solicited for a celebratory Focus Issue on Relativity, “Spacetime 100 Years Later,” to be published in New Journal of Physics. †Internet address: [email protected] ‡On this date the author reached an age which is an integer divisor of the number of references. 1 1 Historical Background Black holes are perhaps the most perfectly thermal objects in the universe, and yet their thermal properties are not fully understood. They are described very accurately by a small number of macroscopic parameters (e.g., mass, angular mo- mentum, and charge), but the microscopic degrees of freedom that lead to their thermal behavior have not yet been adequately identified. Strong hints of the thermal properties of black holes came from the behavior of their macroscopic properties that were formalized in the (classical) four laws of black hole mechanics [1], which have analogues in the corresponding four laws of thermodynamics: The zeroth law of black hole mechanics is that the surface gravity κ of a stationary black hole is constant over its event horizon [2, 1]. -
The University of Tokyo's Newly Founded Institute for the Physics
hosted by IPMU was held on 17 - 21 with new projects. The success of the News December 2007. The workshop,“ Focus workshop also clarified the importance Week on LHC Phenomenology”, was of follow-up visitor programs, such as organized by Mihoko Nojiri (PI of IPMU) one month stays to finalize the projects and held at the IPMU, Research Center started in this meeting.” Building, on the Kashiwa campus. Many theorists found the discussion The Large Hadron Collider (LHC) at with experimentalists extremely CERN in Switzerland will start operating important, and vice verse.“ We in 2008. The aim of the meeting was to developed a consensus that it is bring together leading experimentalists important to set a series of workshops and phenomenologists working on LHC, to understand phenomena at the LHC to come up with new idea on physics and to maximize the performance of beyond the standard model. To reach the new physics searches,”remarked Launch of IPMU this goal, it is necessary to understand Nojiri. The University of Tokyo’s newly phenomena in the standard model: founded Institute for the Physics and deep theoretical understanding of the Mathematics of the Universe (IPMU) , standard model, and thus processes was launched on October 1, 2007. and responses involved in the LHC IPMU has been approved as one of the experiments, is essential to identify World Premier International Research effects of the new physics in the Center Initiatives (WPI) of the Ministry experiments. of Education, Culture, Sports, Science The following invited speakers with a and Technology (MEXT). IPMU is an range of expertise were invited. -
Emergence and Correspondence for String Theory Black Holes
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Philsci-Archive Emergence and Correspondence for String Theory Black Holes Jeroen van Dongen,1;2 Sebastian De Haro,2;3;4;5 Manus Visser,1 and Jeremy Butterfield3 1Institute for Theoretical Physics, University of Amsterdam 2Vossius Center for the History of Humanities and Sciences, University of Amsterdam 3Trinity College, Cambridge 4Department of History and Philosophy of Science, University of Cambridge 5Black Hole Initiative, Harvard University April 5, 2019 Abstract This is one of a pair of papers that give a historical-cum-philosophical analysis of the endeavour to understand black hole entropy as a statistical mechanical entropy obtained by counting string-theoretic microstates. Both papers focus on Andrew Strominger and Cumrun Vafa's ground-breaking 1996 calculation, which analysed the black hole in terms of D-branes. The first paper gives a conceptual analysis of the Strominger-Vafa argument, and of several research efforts that it engendered. In this paper, we assess whether the black hole should be considered as emergent from the D-brane system, particularly in light of the role that duality plays in the argument. We further identify uses of the quantum-to- classical correspondence principle in string theory discussions of black holes, and compare these to the heuristics of earlier efforts in theory construction, in particular those of the old quantum theory. Contents 1 Introduction 3 2 Counting Black Hole Microstates in String Theory 4 3 The Ontology of Black Hole Microstates 8 4 Emergence of Black Holes in String Theory 13 4.1 The conception of emergence . -
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.