Closed String Tachyons on Ads Orbifolds and Dual Yang-Mills
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A Space-Time Orbifold: a Toy Model for a Cosmological Singularity
hep-th/0202187 UPR-981-T, HIP-2002-07/TH A Space-Time Orbifold: A Toy Model for a Cosmological Singularity Vijay Balasubramanian,1 ∗ S. F. Hassan,2† Esko Keski-Vakkuri,2‡ and Asad Naqvi1§ 1David Rittenhouse Laboratories, University of Pennsylvania Philadelphia, PA 19104, U.S.A. 2Helsinki Institute of Physics, P.O.Box 64, FIN-00014 University of Helsinki, Finland Abstract We explore bosonic strings and Type II superstrings in the simplest time dependent backgrounds, namely orbifolds of Minkowski space by time reversal and some spatial reflections. We show that there are no negative norm physi- cal excitations. However, the contributions of negative norm virtual states to quantum loops do not cancel, showing that a ghost-free gauge cannot be chosen. The spectrum includes a twisted sector, with strings confined to a “conical” sin- gularity which is localized in time. Since these localized strings are not visible to asymptotic observers, interesting issues arise regarding unitarity of the S- matrix for scattering of propagating states. The partition function of our model is modular invariant, and for the superstring, the zero momentum dilaton tad- pole vanishes. Many of the issues we study will be generic to time-dependent arXiv:hep-th/0202187v2 19 Apr 2002 cosmological backgrounds with singularities localized in time, and we derive some general lessons about quantizing strings on such spaces. 1 Introduction Time-dependent space-times are difficult to study, both classically and quantum me- chanically. For example, non-static solutions are harder to find in General Relativity, while the notion of a particle is difficult to define clearly in field theory on time- dependent backgrounds. -
Deformations of G2-Structures, String Dualities and Flat Higgs Bundles Rodrigo De Menezes Barbosa University of Pennsylvania, [email protected]
University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2019 Deformations Of G2-Structures, String Dualities And Flat Higgs Bundles Rodrigo De Menezes Barbosa University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Mathematics Commons, and the Quantum Physics Commons Recommended Citation Barbosa, Rodrigo De Menezes, "Deformations Of G2-Structures, String Dualities And Flat Higgs Bundles" (2019). Publicly Accessible Penn Dissertations. 3279. https://repository.upenn.edu/edissertations/3279 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/3279 For more information, please contact [email protected]. Deformations Of G2-Structures, String Dualities And Flat Higgs Bundles Abstract We study M-theory compactifications on G2-orbifolds and their resolutions given by total spaces of coassociative ALE-fibrations over a compact flat Riemannian 3-manifold Q. The afl tness condition allows an explicit description of the deformation space of closed G2-structures, and hence also the moduli space of supersymmetric vacua: it is modeled by flat sections of a bundle of Brieskorn-Grothendieck resolutions over Q. Moreover, when instanton corrections are neglected, we obtain an explicit description of the moduli space for the dual type IIA string compactification. The two moduli spaces are shown to be isomorphic for an important example involving A1-singularities, and the result is conjectured to hold in generality. We also discuss an interpretation of the IIA moduli space in terms of "flat Higgs bundles" on Q and explain how it suggests a new approach to SYZ mirror symmetry, while also providing a description of G2-structures in terms of B-branes. -
Jhep05(2019)105
Published for SISSA by Springer Received: March 21, 2019 Accepted: May 7, 2019 Published: May 20, 2019 Modular symmetries and the swampland conjectures JHEP05(2019)105 E. Gonzalo,a;b L.E. Ib´a~neza;b and A.M. Urangaa aInstituto de F´ısica Te´orica IFT-UAM/CSIC, C/ Nicol´as Cabrera 13-15, Campus de Cantoblanco, 28049 Madrid, Spain bDepartamento de F´ısica Te´orica, Facultad de Ciencias, Universidad Aut´onomade Madrid, 28049 Madrid, Spain E-mail: [email protected], [email protected], [email protected] Abstract: Recent string theory tests of swampland ideas like the distance or the dS conjectures have been performed at weak coupling. Testing these ideas beyond the weak coupling regime remains challenging. We propose to exploit the modular symmetries of the moduli effective action to check swampland constraints beyond perturbation theory. As an example we study the case of heterotic 4d N = 1 compactifications, whose non-perturbative effective action is known to be invariant under modular symmetries acting on the K¨ahler and complex structure moduli, in particular SL(2; Z) T-dualities (or subgroups thereof) for 4d heterotic or orbifold compactifications. Remarkably, in models with non-perturbative superpotentials, the corresponding duality invariant potentials diverge at points at infinite distance in moduli space. The divergence relates to towers of states becoming light, in agreement with the distance conjecture. We discuss specific examples of this behavior based on gaugino condensation in heterotic orbifolds. We show that these examples are dual to compactifications of type I' or Horava-Witten theory, in which the SL(2; Z) acts on the complex structure of an underlying 2-torus, and the tower of light states correspond to D0-branes or M-theory KK modes. -
Limits on New Physics from Black Holes Arxiv:1309.0530V1
Limits on New Physics from Black Holes Clifford Cheung and Stefan Leichenauer California Institute of Technology, Pasadena, CA 91125 Abstract Black holes emit high energy particles which induce a finite density potential for any scalar field φ coupling to the emitted quanta. Due to energetic considerations, φ evolves locally to minimize the effective masses of the outgoing states. In theories where φ resides at a metastable minimum, this effect can drive φ over its potential barrier and classically catalyze the decay of the vacuum. Because this is not a tunneling process, the decay rate is not exponentially suppressed and a single black hole in our past light cone may be sufficient to activate the decay. Moreover, decaying black holes radiate at ever higher temperatures, so they eventually probe the full spectrum of particles coupling to φ. We present a detailed analysis of vacuum decay catalyzed by a single particle, as well as by a black hole. The former is possible provided large couplings or a weak potential barrier. In contrast, the latter occurs much more easily and places new stringent limits on theories with hierarchical spectra. Finally, we comment on how these constraints apply to the standard model and its extensions, e.g. metastable supersymmetry breaking. arXiv:1309.0530v1 [hep-ph] 2 Sep 2013 1 Contents 1 Introduction3 2 Finite Density Potential4 2.1 Hawking Radiation Distribution . .4 2.2 Classical Derivation . .6 2.3 Quantum Derivation . .8 3 Catalyzed Vacuum Decay9 3.1 Scalar Potential . .9 3.2 Point Particle Instability . 10 3.3 Black Hole Instability . 11 3.3.1 Tadpole Instability . -
Tachyon-Dilaton Inflation As an Α'-Non Perturbative Solution in First
Anna Kostouki Work in progress with J. Alexandre and N. Mavromatos TachyonTachyon --DilatonDilaton InflationInflation asas anan αα''--nonnon perturbativeperturbative solutionsolution inin firstfirst quantizedquantized StringString CosmologyCosmology Oxford, 23 September 2008 A. Kostouki 2 nd UniverseNet School, Oxford, 23/09/08 1 OutlineOutline • Motivation : String Inflation in 4 dimensions • Closed Bosonic String in Graviton, Dilaton and Tachyon Backgrounds; a non – perturbative configuration • Conformal Invariance of this model • Cosmological Implications of this model: FRW universe & inflation (under conditions) • Open Issues: Exit from the inflationary phase; reheating A. Kostouki 2 nd UniverseNet School, Oxford, 23/09/08 2 MotivationMotivation Inflation : • elegant & simple idea • explains many cosmological observations (e.g. “horizon problem”, large - scale structure) Inflation in String Theory: • effective theory • in traditional string theories: compactification of extra dimensions of space-time is needed • other models exist too, but no longer “simple & elegant” A. Kostouki 2 nd UniverseNet School, Oxford, 23/09/08 3 ProposalProposal • Closed Bosonic String • graviton, dilaton and tachyon background • field configuration non-perturbative in Does it satisfy conformal invariance conditions? A. Kostouki 2 nd UniverseNet School, Oxford, 23/09/08 4 ConformalConformal propertiesproperties ofof thethe configurationconfiguration General field redefinition: • Theory is invariant • The Weyl anomaly coefficients transform : ( ) A. Kostouki 2 nd UniverseNet School, Oxford, 23/09/08 5 ConformalConformal propertiesproperties ofof thethe configurationconfiguration • 1-loop beta-functions: homogeneous dependence on X0, besides one term in the tachyon beta-function • Power counting → Every other term that appears at higher loops in the beta-functions is homogeneous A. Kostouki 2 nd UniverseNet School, Oxford, 23/09/08 6 ConformalConformal propertiesproperties ofof thethe configurationconfiguration One can find a general field redefinition , that: 1. -
Arxiv:Hep-Th/9404101V3 21 Nov 1995
hep-th/9404101 April 1994 Chern-Simons Gauge Theory on Orbifolds: Open Strings from Three Dimensions ⋆ Petr Horavaˇ ∗ Enrico Fermi Institute University of Chicago 5640 South Ellis Avenue Chicago IL 60637, USA ABSTRACT Chern-Simons gauge theory is formulated on three dimensional Z2 orbifolds. The locus of singular points on a given orbifold is equivalent to a link of Wilson lines. This allows one to reduce any correlation function on orbifolds to a sum of more complicated correlation functions in the simpler theory on manifolds. Chern-Simons theory on manifolds is known arXiv:hep-th/9404101v3 21 Nov 1995 to be related to 2D CFT on closed string surfaces; here I show that the theory on orbifolds is related to 2D CFT of unoriented closed and open string models, i.e. to worldsheet orb- ifold models. In particular, the boundary components of the worldsheet correspond to the components of the singular locus in the 3D orbifold. This correspondence leads to a simple identification of the open string spectra, including their Chan-Paton degeneration, in terms of fusing Wilson lines in the corresponding Chern-Simons theory. The correspondence is studied in detail, and some exactly solvable examples are presented. Some of these examples indicate that it is natural to think of the orbifold group Z2 as a part of the gauge group of the Chern-Simons theory, thus generalizing the standard definition of gauge theories. E-mail address: [email protected] ⋆∗ Address after September 1, 1994: Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544. 1. Introduction Since the first appearance of the notion of “orbifolds” in Thurston’s 1977 lectures on three dimensional topology [1], orbifolds have become very appealing objects for physicists. -
An Introduction to Orbifolds
An introduction to orbifolds Joan Porti UAB Subdivide and Tile: Triangulating spaces for understanding the world Lorentz Center November 2009 An introduction to orbifolds – p.1/20 Motivation • Γ < Isom(Rn) or Hn discrete and acts properly discontinuously (e.g. a group of symmetries of a tessellation). • If Γ has no fixed points ⇒ Γ\Rn is a manifold. • If Γ has fixed points ⇒ Γ\Rn is an orbifold. An introduction to orbifolds – p.2/20 Motivation • Γ < Isom(Rn) or Hn discrete and acts properly discontinuously (e.g. a group of symmetries of a tessellation). • If Γ has no fixed points ⇒ Γ\Rn is a manifold. • If Γ has fixed points ⇒ Γ\Rn is an orbifold. ··· (there are other notions of orbifold in algebraic geometry, string theory or using grupoids) An introduction to orbifolds – p.2/20 Examples: tessellations of Euclidean plane Γ= h(x, y) → (x + 1, y), (x, y) → (x, y + 1)i =∼ Z2 Γ\R2 =∼ T 2 = S1 × S1 An introduction to orbifolds – p.3/20 Examples: tessellations of Euclidean plane Rotations of angle π around red points (order 2) An introduction to orbifolds – p.3/20 Examples: tessellations of Euclidean plane Rotations of angle π around red points (order 2) 2 2 An introduction to orbifolds – p.3/20 Examples: tessellations of Euclidean plane Rotations of angle π around red points (order 2) 2 2 2 2 2 2 2 2 2 2 2 2 An introduction to orbifolds – p.3/20 Example: tessellations of hyperbolic plane Rotations of angle π, π/2 and π/3 around vertices (order 2, 4, and 6) An introduction to orbifolds – p.4/20 Example: tessellations of hyperbolic plane Rotations of angle π, π/2 and π/3 around vertices (order 2, 4, and 6) 2 4 2 6 An introduction to orbifolds – p.4/20 Definition Informal Definition • An orbifold O is a metrizable topological space equipped with an atlas modelled on Rn/Γ, Γ < O(n) finite, with some compatibility condition. -
Tachyon Condensation with B-Field
Oct 2006 KUNS-2042 Tachyon Condensation with B-field Takao Suyama 1 Department of Physics, Kyoto University, Kitashirakawa, Kyoto 606-8502, Japan arXiv:hep-th/0610127v2 13 Nov 2006 Abstract We discuss classical solutions of a graviton-dilaton-Bµν-tachyon system. Both constant tachyon so- lutions, including AdS3 solutions, and space-dependent tachyon solutions are investigated, and their possible implications to closed string tachyon condensation are argued. The stability issue of the AdS3 solutions is also discussed. 1e-mail address: [email protected] 1 1 Introduction Closed string tachyon condensation has been discussed recently [1][2]. However, the understanding of this phenomenon is still under progress, compared with the open string counterpart [3]. A reason for the difficulty would be the absence of a useful tool to investigate closed string tachyon condensation. It is desired that there would be a non-perturbative framework for this purpose. Closed string field theory was applied to the tachyon condensation in string theory on orbifolds, and preliminary results were obtained [4], but the analysis would be more complicated than that in the open string case. To make a modest step forward, a classical gravitational theory coupled to a tachyon was discussed as a leading order approximation to the closed string field theory [5][6][7][8]. In [5][7][8], a theory of graviton, dilaton and tachyon was discussed, and its classical time evolution was investigated. In this paper, we investigate a similar theory, with NS-NS B-field also taken into account. By the presence of the B-field, an AdS3 background is allowed as a classical solution, in addition to the well- known linear dilaton solution. -
Tachyonic Dark Matter
Tachyonic dark matter P.C.W. Davies Australian Centre for Astrobiology Macquarie University, New South Wales, Australia 2109 [email protected] Abstract Recent attempts to explain the dark matter and energy content of the universe have involved some radical extensions of standard physics, including quintessence, phantom energy, additional space dimensions and variations in the speed of light. In this paper I consider the possibility that some dark matter might be in the form of tachyons. I show that, subject to some reasonable assumptions, a tachyonic cosmological fluid would produce distinctive effects, such as a surge in quantum vacuum energy and particle creation, and a change in the conventional temperature-time relation for the normal cosmological material. Possible observational consequences are discussed. Keywords: tachyons, cosmological models, dark matter 1 1. Tachyons in an expanding universe In this section I consider the behaviour of a tachyon in an expanding universe, following the treatment in Davies (1975). A tachyon is a particle with imaginary mass iµ (µ real and positive), velocity v > c and momentum and energy given in a local inertial frame by p = µv(v2 – 1)-1/2 (1.1) E = µ(v2 – 1)-1/2 (1.2) where here and henceforth I choose units with c = ħ =1. Consider such a particle moving in a Friedmann-Roberston-Walker (FRW) universe with scale factor a(t), t being the cosmic time. In a short time dt, the particle will have moved a distance vdt to a point where the local comoving frame is retreating at a speed dv = (a′/a)vdt, where a′ = da/dt. -
Non-Tachyonic Semi-Realistic Non-Supersymmetric Heterotic-String Vacua
Eur. Phys. J. C (2016) 76:208 DOI 10.1140/epjc/s10052-016-4056-2 Regular Article - Theoretical Physics Non-tachyonic semi-realistic non-supersymmetric heterotic-string vacua Johar M. Ashfaquea, Panos Athanasopoulosb, Alon E. Faraggic, Hasan Sonmezd Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK Received: 1 December 2015 / Accepted: 31 March 2016 / Published online: 15 April 2016 © The Author(s) 2016. This article is published with open access at Springerlink.com Abstract The heterotic-string models in the free fermionic 1 Introduction formulation gave rise to some of the most realistic-string models to date, which possess N = 1 spacetime supersym- The discovery of the agent of electroweak symmetry break- metry. Lack of evidence for supersymmetry at the LHC insti- ing at the LHC [1,2] is a pivotal moment in particle physics. gated recent interest in non-supersymmetric heterotic-string While confirmation of this agent as the Standard Model vacua. We explore what may be learned in this context from electroweak doublet representation will require experimental the quasi-realistic free fermionic models. We show that con- scrutiny in the decades to come, the data to date seems to vin- structions with a low number of families give rise to pro- dicate this possibility. Substantiation of this interpretation of liferation of a priori tachyon producing sectors, compared to the data will reinforce the view that the electroweak symme- the non-realistic examples, which typically may contain only try breaking mechanism is intrinsically perturbative, and that one such sector. The reason being that in the realistic cases the SM provides a viable perturbative parameterisation up to the internal six dimensional space is fragmented into smaller the Planck scale. -
Ads Orbifolds and Penrose Limits
IPM/P-2002/061 UCB-PTH-02/54 LBL-51767 hep-th/yymmnnn AdS orbifolds and Penrose limits Mohsen Alishahihaa, Mohammad M. Sheikh-Jabbarib and Radu Tatarc a Institute for Studies in Theoretical Physics and Mathematics (IPM) P.O.Box 19395-5531, Tehran, Iran e-mail: [email protected] b Department of Physics, Stanford University 382 via Pueblo Mall, Stanford CA 94305-4060, USA e-mail: [email protected] c Department of Physics, 366 Le Conte Hall University of California, Berkeley, CA 94720 and Lawrence Berkeley National Laboratory Berkeley, CA 94720 email:[email protected] Abstract In this paper we study the Penrose limit of AdS5 orbifolds. The orbifold can be either in the pure spatial directions or space and time directions. For the AdS =¡ S5 spatial orbifold we observe that after the Penrose limit we 5 £ obtain the same result as the Penrose limit of AdS S5=¡. We identify the 5 £ corresponding BMN operators in terms of operators of the gauge theory on R £ S3=¡. The semi-classical description of rotating strings in these backgrounds have also been studied. For the spatial AdS orbifold we show that in the quadratic order the obtained action for the fluctuations is the same as that in S5 orbifold, however, the higher loop correction can distinguish between two cases. 1 Introduction In the past ¯ve years important results have been obtained relating closed and open string theories, in particular the AdS/CFT correspondence [1] had important impact into the understanding between these two sectors. The main problem in testing the conjecture beyond the supergravity level is the fact that we do not know how to quantize string theory in the presence of RR-fluxes. -
K3 Surfaces and String Duality
RU-96-98 hep-th/9611137 November 1996 K3 Surfaces and String Duality Paul S. Aspinwall Dept. of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855 ABSTRACT The primary purpose of these lecture notes is to explore the moduli space of type IIA, type IIB, and heterotic string compactified on a K3 surface. The main tool which is invoked is that of string duality. K3 surfaces provide a fascinating arena for string compactification as they are not trivial spaces but are sufficiently simple for one to be able to analyze most of their properties in detail. They also make an almost ubiquitous appearance in the common statements concerning string duality. We arXiv:hep-th/9611137v5 7 Sep 1999 review the necessary facts concerning the classical geometry of K3 surfaces that will be needed and then we review “old string theory” on K3 surfaces in terms of conformal field theory. The type IIA string, the type IIB string, the E E heterotic string, 8 × 8 and Spin(32)/Z2 heterotic string on a K3 surface are then each analyzed in turn. The discussion is biased in favour of purely geometric notions concerning the K3 surface itself. Contents 1 Introduction 2 2 Classical Geometry 4 2.1 Definition ..................................... 4 2.2 Holonomy ..................................... 7 2.3 Moduli space of complex structures . ..... 9 2.4 Einsteinmetrics................................. 12 2.5 AlgebraicK3Surfaces ............................. 15 2.6 Orbifoldsandblow-ups. .. 17 3 The World-Sheet Perspective 25 3.1 TheNonlinearSigmaModel . 25 3.2 TheTeichm¨ullerspace . .. 27 3.3 Thegeometricsymmetries . .. 29 3.4 Mirrorsymmetry ................................. 31 3.5 Conformalfieldtheoryonatorus . ... 33 4 Type II String Theory 37 4.1 Target space supergravity and compactification .