Gravidade de Lovelock e a correspondncia AdS/ .Gravidade de Lovelock e a correspondncia AdS/CFT

download Gravidade de Lovelock e a correspondncia AdS/ .Gravidade de Lovelock e a correspondncia AdS/CFT

If you can't read please download the document

  • date post

    30-Dec-2018
  • Category

    Documents

  • view

    212
  • download

    0

Embed Size (px)

Transcript of Gravidade de Lovelock e a correspondncia AdS/ .Gravidade de Lovelock e a correspondncia AdS/CFT

Universidade de So PauloInstituto de Fsica

Gravidade de Lovelock e a correspondnciaAdS/CFT

Anderson Seigo Misobuchi

Orientador: Prof. Dr. Diego Trancanelli

Dissertao apresentada ao Instituto de Fsica da Uni-versidade de So Paulo como requisito para o ttulode Mestre em Cincias

Comisso examinadora:

Prof. Dr. Diego Trancanelli (USP)Prof. Dr. Betti Hartmann (USP)Prof. Dr. Horatiu Nastase (UNESP)

So Paulo2016

FICHA CATALOGRFICAPreparada pelo Servio de Biblioteca e Informaodo Instituto de Fsica da Universidade de So Paulo

Misobuchi, Anderson Seigo

Gravidade de Lovelock e a correspondncia AdS/CFT. So Paulo, 2016. Dissertao (Mestrado) Universidade de So Paulo. Instituto de Fsica. Depto. de Fsica Matemtica. Orientador: Prof. Dr. Diego Trancanelli rea de Concentrao: Teoria de Cordas. Unitermos: 1. Fsica de alta energia; 2. Fsica terica; 3. Teoria de gauge.

USP/IF/SBI-019/2016

University of So PauloPhysics Institute

Lovelock gravity and the AdS/CFTcorrespondence

Anderson Seigo Misobuchi

Advisor: Prof. Dr. Diego Trancanelli

Dissertation presented to the Physics Institute of Uni-versity of So Paulo as a requirement to the title ofMaster of Science

Examining committee:

Prof. Dr. Diego Trancanelli (USP)Prof. Dr. Betti Hartmann (USP)Prof. Dr. Horatiu Nastase (UNESP)

So Paulo2016

Acknowledgements

First of all, I would like to express my sincere gratitude to my advisor Prof. DiegoTrancanelli for all he have taught me. I am indebted to him for stimulating my interestin theoretical physics and for his guidance that helped me in all the time of research andwriting of this thesis.

I thank Prof. Gustavo Burdman, with whom I have learned the principles of quantumfield theory.

I thank all my colleagues at the Physics Institute who made it such a delightful placeto work. In particular, I am grateful to Viktor Jahnke for the fruitful discussions duringour collaboration. A special thanks goes to Renato Critelli, whom I have known for sucha long time and who have been a great friend to me.

I thank FAPESP for the financial support under grant 2014/07840-7.I thank Thain for her nice advices.Special thanks to Bia, the person who is always there to eat japanese food with me.Finally, I want to thank my parents Maria and Carlos, and my sister Katia, whose

unconditional love and support have made everything possible.

ii

Resumo

Misobuchi, A.S. Gravidade de Lovelock e a correspondncia AdS/CFT. Disser-tao de mestrado - Instituto de Fsica, Universidade de So Paulo, So Paulo, 2016.

A correspondncia AdS/CFT uma notvel ferramenta no estudo de teorias de gaugefortemente acopladas que podem ser mapeadas em uma descrio gravitacional dual fra-camente acoplada. A correspondncia melhor entendida no limite em que ambos N e, o rank do grupo de gauge e o acoplamento de t Hooft da teoria de gauge, respectiva-mente, so infinitos. Levar em considerao interaes com termos de curvatura de ordemsuperior nos permite considerar correes de finito. Por exemplo, a primeira correode acoplamento finito para supergravidade tipo IIB surge como um termo de curvaturacom forma esquemtica 3R4.

Neste trabalho investigamos correes de curvatura no contexto da gravidade de Love-lock, que um cenrio simples para investigar tais correes pois as suas equaes demovimento ainda so de segunda ordem em derivadas. Esse cenrio tambm particular-mente interessante do ponto de vista da correspondncia AdS/CFT devido a sua grandeclasse de solues de buracos negros assintoticamente AdS.

Consideramos um sistema de gravidade AdS-axion-dilaton em cinco dimenses comum termo de Gauss-Bonnet e encontramos uma soluo das equaes de movimento, oque corresponde a uma black brane exibindo uma anisotropia espacial, onde a fonte daanisotropia um campo escalar linear em uma das coordenadas espaciais. Estudamos suaspropriedades termodinmicas e realizamos a renormalizao hologrfica usando o mtodode Hamilton-Jacobi. Finalmente, usamos a soluo obtida como dual gravitacional deum plasma anisotrpico fortemente acoplado com duas cargas centrais independentes,a 6= c. Calculamos vrios observveis relevantes para o estudo do plasma, a saber, aviscosidade de cisalhamento sobre densidade de entropia, a fora de arrasto, o parmetrode jet quenching, o potencial entre um par quark-antiquark e a taxa de produo de ftons.

Palavras-chave: correspondncia gauge-gravidade, holografia e o plasma de quark e glu-ons, gravidade de curvatura mais elevada.

iii

Abstract

Misobuchi, A.S. Lovelock Gravity and the AdS/CFT correspondence 2016. Masterdegree dissertation - Physics Institute, University of So Paulo, So Paulo, 2016.

The AdS/CFT correspondence is a remarkable tool in the study of strongly coupledgauge theories which can be mapped to a dual, weakly coupled gravitational description.The correspondence is best understood in the limit in which both N and , the rank ofthe gauge group and the t Hooft coupling of the gauge theory, respectively, are infinite.Accounting for higher curvature interactions allows one to begin to consider finite . Forexample, the leading finite coupling corrections to type IIB supergravity arise as stringycorrections with schematic form 3R4.

In this work we investigate higher curvature corrections in a simpler scenario, the Love-lock gravity. Lovelock gravity is a nice framework to investigate such corrections since itsequations of motion are still second order in derivatives and is particularly interesting fromthe point of view of the AdS/CFT correspondence because a large class of asymptoticallyAdS black holes solutions are known.

We consider five-dimensional AdS-axion-dilaton gravity with a Gauss-Bonnet termand find a solution of the equations of motion which corresponds to a black brane exhibit-ing a spatial anisotropy, with the source of the anisotropy being an axion field linear inone of the spatial coordinates. We study its thermodynamics and we carry out the holo-graphic renormalization using the Hamilton-Jacobi approach. Finally, we use the solutionas a gravity dual to a strongly coupled anisotropic plasma with two independent centralcharges, a 6= c. We compute several observables relevant to the study of the plasma,namely, the shear viscosity over entropy density ratio, the drag force, the jet quenchingparameter, the quarkonium potential and the thermal photon production.

Keywords: Gauge-gravity correspondence, Holography and quark-gluon plasmas, Highercurvature gravity.

iv

Contents

List of Figures vii

List of Tables ix

1 Overview 1

2 AdS/CFT correspondence 42.1 Arguments for plausibility . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Basics of string theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.2 Superstring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.3 Type IIB supergravity . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 D-branes: the two pictures . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.1 Open string picture . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.2 Closed string picture . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Statement of the AdS/CFT correspondence . . . . . . . . . . . . . . . . . 182.5 Correlation functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3 Lovelock gravity 213.1 Non-coordinate basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Lovelock action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3 Equations of motion and vacuum solutions . . . . . . . . . . . . . . . . . . 243.4 Black hole solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.5 Gauss-Bonnet black holes . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.6 Lovelock and AdS/CFT correspondence . . . . . . . . . . . . . . . . . . . . 27

3.6.1 Violation of the KSS bound . . . . . . . . . . . . . . . . . . . . . . 283.6.2 Unitarity of the dual CFT . . . . . . . . . . . . . . . . . . . . . . . 283.6.3 Positivity of the energy flux . . . . . . . . . . . . . . . . . . . . . . 303.6.4 Causality violation . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

v

CONTENTS vi

4 Chern-Simons diffusion rate from higher curvature gravity 344.1 Chern-Simons diffusion rate . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2 Gravity setup and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Anisotropic black branes in higher curvature gravity 415.1 Action and solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2 Holographic renormalization . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.2.1 Radial evolution Hamiltonian . . . . . . . . . . . . . . . . . . . . . 465.2.2 Recursive method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.2.3 Fefferman-Graham expansions . . . . . . . . . . . . . . . . . . . . . 535.2.4 The 1-point functions . . . . . . . . . . . . . . . . . . . . . . . . . . 545.2.5 Central charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.3 Boundary stress tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6 Probing strongly coupled anisotropic plasmas from higher curvatureg