DOCSLIB.ORG

Field-To-Particle Transition and Nonminimal Particles in Sigma Model, Dilaton Gravity and Gauged Supergravity

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Field-To-Particle Transition and Nonminimal Particles in Sigma Model, Dilaton Gravity and Gauged Supergravity 25 October 2001 Physics Letters B 519 (2001) 111–120 www.elsevier.com/locate/npe Field-to-particle transition and nonminimal particles in sigma model, dilaton gravity and gauged supergravity Konstantin G. Zloshchastiev Department of Physics, National University of Singapore, Singapore 117542, Republic of Singapore and Department of Theoretical Physics, Dnepropetrovsk State University, Dnepropetrovsk 49050, Ukraine Received 19 July 2001; received in revised form 19 August 2001; accepted 28 August 2001 Editor: T. Yanagida Abstract The field-to-particle transition formalism is applied to the sigma model, and then to the 2D dilaton gravity and gauged supergravity 0-brane solutions. This approach yields the method of the consistent quantization in the vicinity of the nontrivial vacuum induced by a field solution, as well as the recipe of the nontrivial dynamical dimensional reduction which takes into account field fluctuations. It is explicitly shown that in all cases the end product is the so-called nonminimal point particle—an object whose action depends on the world-line curvature. Such objects are suspected to be common at early stages of evolution of the Universe. 2001 Elsevier Science B.V. All rights reserved. PACS: 04.60.Kz; 04.65.+e; 11.25.Sq; 11.27.+d; 12.60.Jv 1. Introduction plain bosonic string in the N-dimensional space–time. The remainder of that section is devoted to quantiza- The studies of the field-to-particle transition grew tion of the obtained effective action as a constrained up from the old program of constructing a theory mechanics with higher derivatives. There we discuss which does not contain matter as an external postu- the recent state of the theory and calculate the quantum lated entity but consider fields as sources of matter corrections to the mass of such a field/string-induced and the particles as special field configurations. How- particle [1]. ever, if one tries to fit a field solution into the particle Further, the 2D gravity [2], which can be viewed interpretation, one encounters eventually the problem also as a dimensional reduction of the 3D BTZ black of how to deal with the field fluctuations. Then it is hole and spherically symmetric solution of 4D dilaton necessary to correctly handle the circumstance that a Einstein–Maxwell gravity, seems to be a good place field solution has an infinite number of degrees of free- for demonstration of the approach on classical and dom, unlike a particle. In Section 2 we demonstrate the quantum level. field-to-particle transition for the soliton-like solutions Finally, in Section 4 we demonstrate how gauged of the N-component 2D sigma model or, equivalently, supergravity 0-brane solutions can be also described in terms of the mechanics of nonminimal particles with rigidity. The latter is invariant under the transforma- E-mail address: [email protected] (K.G. Zloshchastiev). tions of the proper parameter s, so one may recall an- 0370-2693/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII:S0370-2693(01)01087-5 112 K.G. Zloshchastiev / Physics Letters B 519 (2001) 111–120 other diff-invariant candidates for the role of a 0-brane coinciding with the total energy up to the sign and boundary theory, e.g., the generalized conformal me- Lorentz factor γ (below the boundaries ρi will be chanics of a probe 0-brane [3,4]. However, the probe omitted for brevity). mechanics by construction takes into account neither Let us change to the set of the collective coordinates the field fluctuations near the brane solution nor aris- {σ0 = s,σ1 = ρ} such that ing zero modes, therefore, the nonminimal terms could m = m + m = not arise there in principle. x x (s) e(1)(s)ρ, Xa(x, t) Xa(σ), (2.6) where xm(s) turn out to be the coordinates of a (1+1)- 2. Effective nonminimal-particle action from dimensional point particle, em (s) is the unit spacelike sigma model (1) vector orthogonal to the world-line. Hence, the initial action can be rewritten in new coordinates as In this section, we will construct the nonlinear effective action of the sigma model in the vicinity S[X]= L(X)∆d 2σ, of a localized soliton solution, and then consider its quantum aspects. In fact, here we will describe 1 a b L(X) = σab∂−X ∂+X − U(X), the procedure of the correct transition from field to 2 √ particle degrees of freedom. 1 ∂xm ∂± = ∂ ± ∂ ∆ = = x˙2 ( − where ∆ s ρ , det ∂σk 1 2.1. General formalism ρk), whereas k is the curvature of a particle world-line ε x˙mx¨n = mn Let us begin with the action of the following k √ , (2.7) x˙2 3 N-component 2D sigma model where εmn is the unit antisymmetric tensor. This S[X]= L(X) d2x, (2.1) new action contains the N redundant degrees of freedom which eventually lead to appearance of the where the Lagrangian is given by so-called “zero modes”. To eliminate them we must constrain the model by means of the condition of 1 a ν b L(X) = σab∂ν X ∂ X − U(X), (2.2) vanishing of the functional derivative with respect to 2 field fluctuations about a chosen static solution, and in × where σ is a constant N N matrix, Greek indices run result we will obtain the required effective action. from 0 to 1, and a, b = 1,...,N. The corresponding So, the fluctuations of the fields Xa(σ) in the equations of motion are (s) neighborhood of the static solution Xa (ρ) are given ν b by the expression σab ∂ ∂νX + Ua(X) = 0, (2.3) = ∂U(X) = X (σ) = X(s)(ρ) + δX (σ). (2.8) where we have defined Ua(X) ∂Xa , Uab(X) a a a ∂2 U(X) ∂Xa∂Xb . Suppose, we have the solution which depends Substituting them into the expression (2.7) and con- on the single combination of initial variables, e.g., the (s) sidering the static equations of motion for Xa (ρ) we Lorentz-invariant one: have (below we will omit the superscript “(s)”atX’s (s) = (s) − = − 2 for brevity assuming that all the values are taken on Xa (ρ) Xa γ(x vt) ,γ 1/ 1 v , (2.4) (s) the solutions Xa (ρ)): possessing localized Lagrangian density in the sense that the mass integral over the domain of applicability 2 ∆ a b S[δX]= d σ 2L + σab∂−δX ∂+δX 2 is finite a b a b ρ2 − U δX δX + ∆ σ X δX ab ab µ =− L X(s) dρ < ∞, (2.5) + O δX3 + S,˘ (2.9) ρ1 K.G. Zloshchastiev / Physics Letters B 519 (2001) 111–120 113 where S˘ are surface terms (see below for details), describing the nonminimal point-particle with curva- ture, where µ is the value of the mass integral above, 1 a b L =− σabX X − U, and 2 ρ2 and prime means the derivative with respect to ρ. (0) 1 a b µ α = σabX f dρ = . (2.16) Extremizing this action with respect to δXa one can 2 2 2caˆ obtain the system of equations in partial derivatives for ρ1 field fluctuations: ˘ Let us restore the surface terms S in the action −1 a ac b ∂s ∆ ∂s − ∂ρ ∆∂ρ δX + ∆σ UcbδX (2.15). In general case they are nonzero and give a contribution: a 2 2 + X k x˙ + O δX = 0, (2.10) S =− ds x˙2 µ + α k + α k2 + α k3 , which is the constraint removing redundant degrees eff 1 2 3 of freedom, besides we have denoted the inverse ma- where α =ˇα |ρ2 , αˇ ≡ σ Xa f b,α = α(0) + trix as σ with raised indices. Supposing δXa(s, ρ) = 1 1 ρ1 1 ab 2 2 − ˇ |ρ2 =−1 a b|ρ2 k(s)fa(ρ), in the linear approximations ρk 1 α3 (ρα1) ρ1 ,α3 2 ρσabf f ρ1 .However,the (which naturally guarantees also the smoothness of a natural requirement of vanishing of field fluctuations world-line at ρ → 0, i.e., the absence of a cusp in this at the spatial boundaries leads to the canceling of the point) and O(δX2) = 0 we obtain the system of three terms containing k and k3, as. Thus, below we will ˘ ordinary derivative equations regard the action (2.15), i.e., (2.9) at S = 0, as a basic one. It is straightforward to derive the corresponding 1 d 1 dk √ √ + ck = 0, (2.11) equation of motion in the Frenet basis x˙2 ds x˙2 ds 1 d 1 dk 1 a ac a b a √ √ + − 2 = −f + σ Ucb − cδ f + X = 0, (2.12) c k k 0, (2.17) b x˙2 ds x˙2 ds 2 where c is the constant of separation. Searching for a hence one can see that Eq. (2.11) was nothing but this solution of the last subsystem in the form (we assume equation in the linear approximation with respect to that we can have several c’s and thus no summation curvature, as was expected. over a in this and next formula) Thus, the only problem, which yet demands on resolving is the determination of the concrete (eigen) = + 1 fa ga Xa, (2.13) value of the constant(s) c. It is equivalent to the caˆ eigenvalue problem for the system (2.14) under some we obtain the homogeneous system chosen boundary conditions. If one supposes, for − a + ac − a b = instance, the finiteness of g at infinity then the c’s g σ Ucb caˆ δb g 0.
Load more

Recommended publications
  • Models of Phase Stability in Jackiw-Teitelboim Gravity
    PHYSICAL REVIEW D 100, 124061 (2019) Models of phase stability in Jackiw-Teitelboim gravity Arindam Lala* Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla, 4059 Valparaiso, Chile † Dibakar Roychowdhury Department of Physics, Indian Institute of Technology Roorkee, Roorkee, 247667 Uttarakhand, India (Received 4 October 2019; published 31 December 2019) We construct solutions within Jackiw-Teitelboim (JT) gravity in the presence of nontrivial couplings between the dilaton and the Abelian 1-form where we analyze the asymptotic structure as well as the phase stability corresponding to charged black hole solutions in 1 þ 1 D. We consider the Almheiri-Polchinski model as a specific example within 1 þ 1 D JT gravity which plays a pivotal role in the study of Sachdev-Ye- Kitaev (SYK)/anti–de Sitter (AdS) duality. The corresponding vacuum solutions exhibit a rather different asymptotic structure than their uncharged counterpart. We find interpolating vacuum solutions with AdS2 in the IR and Lifshitz2 in the UV with dynamical exponent zdyn ¼ 3=2. Interestingly, the presence of charge also modifies the black hole geometry from asymptotically AdS to asymptotically Lifshitz with the same value of the dynamical exponent. We consider specific examples, where we compute the corresponding free energy and explore the thermodynamic phase stability associated with charged black hole solutions in 1 þ 1 D. Our analysis reveals the existence of a universal thermodynamic feature that is expected to reveal its immediate consequences on the dual SYK physics at finite density and strong coupling. DOI: 10.1103/PhysRevD.100.124061 I. INTRODUCTION AND MOTIVATIONS For the last couple of years, there has been a systematic For the last couple of decades, there had been consid- effort toward unveiling the dual gravitational counterpart erable efforts toward a profound understanding of the of the SYK model.
    [Show full text]
  • Exact Solutions and Critical Chaos in Dilaton Gravity with a Boundary
    Prepared for submission to JHEP INR-TH-2017-002 Exact solutions and critical chaos in dilaton gravity with a boundary Maxim Fitkevicha;b Dmitry Levkova Yegor Zenkevich1c;d;e aInstitute for Nuclear Research of the Russian Academy of Sciences, 60th October An- niversary Prospect 7a, Moscow 117312, Russia bMoscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudny 141700, Moscow Region, Russia cDipartimento di Fisica, Universit`adi Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy dINFN, sezione di Milano-Bicocca, I-20126 Milano, Italy eNational Research Nuclear University MEPhI, Moscow 115409, Russia E-mail: [email protected], [email protected], [email protected] Abstract: We consider (1 + 1)-dimensional dilaton gravity with a reflecting dy- namical boundary. The boundary cuts off the region of strong coupling and makes our model causally similar to the spherically-symmetric sector of multidimensional gravity. We demonstrate that this model is exactly solvable at the classical level and possesses an on-shell SL(2; R) symmetry. After introducing general classical solution of the model, we study a large subset of soliton solutions. The latter describe reflec- tion of matter waves off the boundary at low energies and formation of black holes at energies above critical. They can be related to the eigenstates of the auxiliary inte- grable system, the Gaudin spin chain. We argue that despite being exactly solvable, the model in the critical regime, i.e. at the verge of black hole formation, displays arXiv:1702.02576v2 [hep-th] 17 Apr 2017 dynamical instabilities specific to chaotic systems. We believe that this model will be useful for studying black holes and gravitational scattering.
    [Show full text]
  • A New Look at the RST Model Jian-Ge Zhoua, F. Zimmerschieda, J
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server A new lo ok at the RST mo del a a a,b Jian-Ge Zhou , F. Zimmerschied , J.{Q. Liang and a H. J. W. Muller{Ki rsten a Department of Physics, University of Kaiserslautern, P. O. Box 3049, D{67653 Kaiserslautern, Germany b Institute of Theoretical Physics, Shanxi University Taiyuan, Shanxi 030006, P. R. China and Institute of Physics, Academia Sinica, Beijing 100080, P. R. China Abstract The RST mo del is augmented by the addition of a scalar eld and a b oundary term so that it is well-p osed and lo cal. Expressing the RST action in terms of the ADM formulation, the constraint structure can b e analysed completely.It is shown that from the view p oint of lo cal eld theories, there exists a hidden dynamical eld in the RST mo del. Thanks to the presence of this hidden 1 dynamical eld, we can reconstruct the closed algebra of the constraints which guarantee the general invariance of the RST action. The resulting stress tensors T are recovered to b e true tensor quantities. Esp ecially, the part of the stress tensors for the hidden dynamical eld gives the precise expression for t . 1 At the quantum level, the cancellation condition for the total central charge is reexamined. Finally, with the help of the hidden dynamical eld , the fact 1 that the semi-classical static solution of the RST mo del has two indep endent parameters (P,M), whereas for the classical CGHS mo del there is only one, can b e explained.
    [Show full text]
  • Fourth Meeting on Constrained Dynamics and Quantum Gravity
    Fourth Meeting on Constrained Dynamics and Quantum Gravity Sardinia | September 2005 Mass and entropy of the exact string black hole speaker: Daniel Grumiller (DG) affiliation: Institute for Theoretical Physics, University of Leipzig, Augustusplatz 10-11, D-04109 Leipzig, Germany supported by an Erwin-Schr¨odinger fellowship, project J-2330-N08 of the Austrian Science Foundation (FWF) Based upon: DG, hep-th/0501208, hep-th/0506175 Outline 1. Motivation/Actions 2. The exact string black hole (ESBH) 3. Action for the ESBH 4. Mass and entropy of the ESBH 5. Loose ends 1 1. Motivation Why 2D? 2 1. Motivation Why 2D? dimensionally reduced models (spherical • symmetry) strings (2D target space) • integrable models (PSM) • models for BH physics (information loss) • study important conceptual problems with- out encountering insurmountable technical ones 2D gravity: useful toy model(s) for classi- ! cal and quantum gravity most prominent member not just a toy model: Schwarzschild Black Hole (\Hydrogen atom of General Relativity") 2-a Actions (2D dilaton gravity) EH: S = dDxp gR + surface Z − R: Ricci scalar g: determinant of metric gµν Physical degrees of freedom: D(D 3)=2 − JBD/scalar-tensor theories/low energy strings: S(2) = dDxp g XR U(X)( X)2 + 2V (X) − − r Z X: \dilaton field” U; V : (arbitrary) potentials \dilaton gravity in D dimensions" Often exponential representation: 2φ X = e− Extremely useful: First order action! In 2D: (1) a a S = XaT +XR+ (XaX U(X) + V (X)) ; Z Review: DG, W. Kummer, D. Vassilevich, hep-th/0204253 3 3. The exact string BH µ NLSM (target space metric: gµν, coordinates: x ) σ 2 ij µ ν S d ξp h gµνh @ x @ x + α φ + tachyon / − i j 0 R Z set B-field zero.
    [Show full text]
  • Black Holes and Thermodynamics-The First Half Century
    Black holes and thermodynamics — The first half century Daniel Grumiller, Robert McNees and Jakob Salzer Abstract Black hole thermodynamics emerged from the classical general relativis- tic laws of black hole mechanics, summarized by Bardeen–Carter–Hawking, to- gether with the physical insights by Bekenstein about black hole entropy and the semi-classical derivation by Hawking of black hole evaporation. The black hole entropy law inspired the formulation of the holographic principle by ’t Hooft and Susskind, which is famously realized in the gauge/gravity correspondence by Mal- dacena, Gubser–Klebanov–Polaykov and Witten within string theory. Moreover, the microscopic derivation of black hole entropy, pioneered by Strominger–Vafa within string theory, often serves as a consistency check for putative theories of quantum gravity. In this book chapter we review these developments over five decades, start- ing in the 1960ies. Introduction and Prehistory Introductory remarks. The history of black hole thermodynamics is intertwined with the history of quantum gravity. In the absence of experimental data capable of probing Planck scale physics the best we can do is to subject putative theories of quantum gravity to stringent consistency checks. Black hole thermodynamics pro- vides a number of highly non-trivial consistency checks. Perhaps most famously, arXiv:1402.5127v3 [gr-qc] 17 Mar 2014 Daniel Grumiller Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria e-mail: [email protected]
    [Show full text]
  • Semi-Classical Black Hole Holography
    Dissertation for the degree of Doctor of Philosophy Semi-Classical Black Hole Holography Lukas Schneiderbauer School of Engineering and Natural Sciences Faculty of Physical Sciences Reykjavík, September 2020 A dissertation presented to the University of Iceland, School of Engineering and Natural Sciences, in candidacy for the degree of Doctor of Philosophy. Doctoral committee Prof. Lárus Thorlacius, advisor Faculty of Physical Sciences, University of Iceland Prof. Þórður Jónsson Faculty of Physical Sciences, University of Iceland Prof. Valentina Giangreco M. Puletti Faculty of Physical Sciences, University of Iceland Prof. Bo Sundborg Department of Physics, Stockholm University Opponents Prof. Veronika Hubeny University of California, Davis Prof. Mukund Rangamani University of California, Davis Semi-classical Black Hole Holography Copyright © 2020 Lukas Schneiderbauer. ISBN: 978-9935-9452-9-7 Author ORCID: 0000-0002-0975-6803 Printed in Iceland by Háskólaprent, Reykjavík, Iceland, September 2020. Contents Abstractv Ágrip (in Icelandic) vii Acknowledgementsx 1 Introduction1 2 Black Hole Model7 2.1 The Polyakov term . .8 2.2 The stress tensor . 11 2.3 Coherent matter states . 14 2.4 The RST term . 15 2.5 Equations of motion . 15 2.6 Black hole thermodynamics . 17 3 Page Curve 21 3.1 Generalized entropy . 24 4 Quantum Complexity 27 4.1 Complexity of black holes . 29 4.2 The geometric dual of complexity . 32 5 Conclusion 35 Bibliography 37 Articles 47 Article I ..................................... 49 iii Article II .................................... 67 Article III .................................... 99 iv Abstract This thesis discusses two aspects of semi-classical black holes. First, a recently improved semi-classical formula for the entanglement entropy of black hole radiation is examined.
    [Show full text]
  • Information Loss in the CGHS Model Fethi Mubin¨ Ramazanoglu˘
    Information Loss in the CGHS Model Fethi Mubin¨ Ramazanoglu˘ PRINCETON UNIVERSITY DEPARTMENT of PHYSICS ILQGS, 03/09/2010 collaborators Abhay Ashtekar, PennState Frans Pretorius, Princeton Information Loss in the CGHS Model Outline 1 A Quick Look at Informaton Loss 2 CGHS Model 3 Numerical Solution 4 Results: Macroscopic BH Finiteness of y− Bondi Mass and Hawking Radiation Diminishing of the Bondi Mass 5 Results: Planck Scale BH 6 Recent 7 Conclusions and Future 2 / 30 MFA Quantum Gravity Information Loss in the CGHS Model A Quick Look at Informaton Loss A Quick Overview of Information Loss I+ I+ L − R y 3 / 30 z− − − IL IR Fixed Background MFA Information Loss in the CGHS Model A Quick Look at Informaton Loss A Quick Overview of Information Loss I+ I+ L − R y 4 / 30 z− − − IL IR Fixed Background Quantum Gravity Information Loss in the CGHS Model A Quick Look at Informaton Loss A Quick Overview of Information Loss I+ I+ L − R y 5 / 30 z− − − IL IR Fixed Background MFA Quantum Gravity Information Loss in the CGHS Model CGHS Model Why CGHS Why 1+1 D? Conformal flatness Easy calculation at 1-loop: Trace anomaly ) Local action More manageable numerics Qualitatively similar to reduced 3+1 D, yet analytical solutions. 6 / 30 Information Loss in the CGHS Model CGHS Model Action and Classical Equations of Motion S(g; φ, f ) = 1 Z d2Ve−2φ R + 4gabr φr φ + 4κ2 G a b N 1 X Z − d2Vgabr f r f 2 a i b i i=1 S(4)(g; φ, f )= 1 Z d2Ve−2φ R + 2gabr φr φ + 2e−2φκ2 G a b N 1 X Z − d2Ve−φgabr f r f 2 a i b i i=1 Callan, Giddings,Harvey, Strominger, Phys.
    [Show full text]
  • Xavier Calmet Editor Quantum Aspects of Black Holes Fundamental Theories of Physics
    Fundamental Theories of Physics 178 Xavier Calmet Editor Quantum Aspects of Black Holes Fundamental Theories of Physics Volume 178 Series editors Henk van Beijeren Philippe Blanchard Paul Busch Bob Coecke Dennis Dieks Detlef Dürr Roman Frigg Christopher Fuchs Giancarlo Ghirardi Domenico J.W. Giulini Gregg Jaeger Claus Kiefer Nicolaas P. Landsman Christian Maes Hermann Nicolai Vesselin Petkov Alwyn van der Merwe Rainer Verch R.F. Werner Christian Wuthrich More information about this series at http://www.springer.com/series/6001 Xavier Calmet Editor Quantum Aspects of Black Holes 123 Editor Xavier Calmet Department of Physics and Astronomy University of Sussex Brighton UK ISBN 978-3-319-10851-3 ISBN 978-3-319-10852-0 (eBook) DOI 10.1007/978-3-319-10852-0 Library of Congress Control Number: 2014951685 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer.
    [Show full text]
  • The Factorization Problem in Jackiw-Teitelboim Gravity
    The factorization problem in Jackiw-Teitelboim gravity The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Harlow, Daniel and Daniel Jafferis. "The factorization problem in Jackiw-Teitelboim gravity." Journal of High Energy Physics 2020, 2 (February 2020): 177 © 2020 The Authors As Published https://doi.org/10.1007/JHEP02(2020)177 Publisher Springer Science and Business Media LLC Version Final published version Citable link https://hdl.handle.net/1721.1/128911 Terms of Use Creative Commons Attribution Detailed Terms https://creativecommons.org/licenses/by/4.0/ Published for SISSA by Springer Received: November 14, 2019 Accepted: February 12, 2020 Published: February 27, 2020 The factorization problem in Jackiw-Teitelboim gravity JHEP02(2020)177 Daniel Harlowa and Daniel Jafferisb aCenter for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02138, U.S.A. bCenter for the Fundamental Laws of Nature, Harvard University, Cambridge, MA 02138, U.S.A. E-mail: [email protected], [email protected] Abstract: In this note we study the 1 + 1 dimensional Jackiw-Teitelboim gravity in Lorentzian signature, explicitly constructing the gauge-invariant classical phase space and the quantum Hilbert space and Hamiltonian. We also semiclassically compute the Hartle- Hawking wave function in two different bases of this Hilbert space. We then use these results to illustrate the gravitational version of the factorization problem of AdS/CFT: the Hilbert space of the two-boundary system tensor-factorizes on the CFT side, which appears to be in tension with the existence of gauge constraints in the bulk.
    [Show full text]
  • GR20/Amaldi10 — Abstract Book
    GR20/Amaldi10 | Abstract Book Local Organising Committee July 6, 2013 Contents A1 - Exact solutions and their interpretation3 Oral session...............................................3 Poster session.............................................. 12 A2 - Mathematical relativity and other progress in classical gravity theory 17 Oral session............................................... 17 Poster session.............................................. 24 A3 - Modified gravity theories 35 Oral session............................................... 35 Poster session.............................................. 43 A4 - Complex and conformal methods in classical and quantum gravity 51 Oral session............................................... 51 Poster session.............................................. 57 B1 - Relativistic astrophysics 59 Oral session............................................... 59 Poster session.............................................. 66 Joint session B2 and B4: Approximate solutions to Einstein equations, Methods and Applications' 74 Oral session............................................... 74 B2 - Numerical relativity and astrophysical applications 78 Oral session............................................... 78 Poster session.............................................. 86 B3 - Numerical relativity : methods, theoretical gravity and high energy applications 88 Oral session............................................... 88 Poster session.............................................. 94 B4 - Analytic approximations,
    [Show full text]
  • From Black Holes to Baby Universes in CGHS Gravity Arxiv:2103.13422V2
    From black holes to baby universes in CGHS gravity Victor Godeta and Charles Marteaub a International Centre for Theoretical Sciences (ICTS-TIFR), Tata Institute of Fundamental Research, Shivakote, Hesaraghatta, Bangalore 560089, India e-mail: [email protected] b Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 0C2, Canada e-mail: [email protected] ABSTRACT. We study CGHS\ gravity, a variant of the matterless Callan-Giddings- Harvey-Strominger model. We show that it describes a universal sector of the near hori- zon perturbations of non-extremal black holes in higher dimensions. In many respects this theory can be viewed as a flat space analog of Jackiw-Teitelboim gravity. The result for the Euclidean path integral implies that CGHS\ is dual to a Gaussian ensemble that we describe in detail. The simplicity of this theory allows us to compute exact quantities such as the quenched free energy and provides a useful playground to study baby universes, averages and factorization. In particular we derive a “wormhole = diagonal” identity. We also give evidence for the existence of a non-perturbative completion in terms of a matrix arXiv:2103.13422v2 [hep-th] 28 Jun 2021 model. Finally, flat wormhole solutions in this model are discussed. 2 1 Introduction3 1.1 Black hole near horizon dynamics . .3 1.2 Euclidean path integral in gravity . .5 1.3 Summary . .7 2 The CGHSd model8 2.1 Review of the model . .8 2.2 Boundary action . .9 2.3 Euclidean path integral . 13 3 Near horizon dynamics of non-extremal black holes 16 3.1 BTZ black hole .
    [Show full text]
  • Callan-Giddings-Harvey-Strominger Vacuum in Loop Quantum Gravity and Singularity Resolution
    Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution Alejandro Corichi,1, 2, ∗ Javier Olmedo,3, 4, y and Saeed Rastgoo5, 1, z 1Centro de Ciencias Matemticás, Universidad Nacional Autónoma de México, Campus Morelia, Apartado Postal 61-3, Morelia, Michoacán 58090, Mexico 2Center for Fundamental Theory, Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, PA 16802, USA 3Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001, USA 4Instituto de Física, Facultad de Ciencias, Iguá 4225, Montevideo, Uruguay 5Departamento de Física, Universidad Autónoma Metropolitana - Iztapalapa San Rafael Atlixco 186, México D.F. 09340, México (Dated: May 9, 2018) We study here a complete quantization of a Callan-Giddings-Harvey-Strominger (CGHS) vacuum model following loop quantum gravity techniques. Concretely, we adopt a formu- lation of the model in terms of a set of new variables that resemble the ones commonly employed in spherically symmetric loop quantum gravity. The classical theory consists of two pairs of canonical variables plus a scalar and diffeomorphism (first class) constraints. We consider a suitable redefinition of the Hamiltonian constraint such that the new constraint algebra (with structure constants) is well adapted to the Dirac quantization approach. For it, we adopt a polymeric representation for both the geometry and the dilaton field. On the one hand, we find a suitable invariant domain of the scalar constraint operator, and we construct explicitly its solution space. There, the eigenvalues of the dilaton and the metric operators cannot vanish locally, allowing us to conclude that singular geometries are ruled out in the quantum theory.
    [Show full text]