An introduction to the gravity fluid correspondence and its applications
This presentation is the property of its rightful owner.
Sponsored Links
1 / 36

An introduction to the Gravity/Fluid correspondence and its applications PowerPoint PPT Presentation


  • 43 Views
  • Uploaded on
  • Presentation posted in: General

An introduction to the Gravity/Fluid correspondence and its applications. Ya-Peng Hu College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 2013.03.28 @ICTS, hefei. Outline. A. Introduction 1) AdS/CFT correspondence : a direct realization of the

Download Presentation

An introduction to the Gravity/Fluid correspondence and its applications

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


An introduction to the gravity fluid correspondence and its applications

An introduction to the Gravity/Fluid correspondence and its applications

Ya-Peng Hu

College of Science, Nanjing University of Aeronautics and Astronautics,

Nanjing 210016, China

2013.03.28 @ICTS, hefei


Outline

Outline

A. Introduction

1) AdS/CFT correspondence : a direct realization of the

Holography principle

2) Gravity/Fluid correspondence: long wavelength limit in

AdS/CFT correspondence; fundamental algorithm and procedure

B. The first order dual hydrodynamics via Gravity/Fluid

correspondence in the Gauss-Bonnet gravity

C. Chern-Simons effects in Gravity/Fluid correspondence:

anomalous magnetic and vortical effects

D. Holographic charged fluid at finite cutoffsurface via

Gravity/Fluid correspondence

E. Conclusion and discussion


A introduction

A. Introduction

1) AdS/CFT correspondence : a direct realization of the Holography principle

  • Entropy of Black hole: S= f(A); S=A/4

  • Holography principle: Gravity in the bulk is equivalent to a gauge theory on the boundary. ‘ t Hooft (‘93), Susskind (‘94)


An introduction to the gravity fluid correspondence and its applications

  • AdS/CFT correspondence:

    Type IIB string theory on AdS5 × S5 dual to

    N = 4 Super-Yang-Mills theory in 3+1 dimensions

  • General formalism: In the approximation of classical (super) gravity

    : classical (super) gravity action

    : boundary values of bulk fields

    : dual CFT operators.


An introduction to the gravity fluid correspondence and its applications

2) Gravity/Fluid correspondence

  • Long wavelength limit in AdS/CFT correspondence: any quantum field effectively described by hydrodynamics; CFT becomes conformal fluid

  • Gravity/Fluid correspondence application: conformal viscous fluid stress tensor can be deduced from the dual gravity (hep-th/0712.2456)

  • Stress tensor of viscous fluid with conformal symmetry broken

  • Stress tensor of conformal viscous fluid


An introduction to the gravity fluid correspondence and its applications

  • Fundamental algorithm and procedure in Gravity/Fluid correspondence:

    Black brane solution  Boosted black brane solution 

    Perturbative black brane solution 

    Boundary stress tensor (or other quantities) in the bulk

    Stress tensor (or other quantities) of the dual fluid on the boundary

  • For example

    Black brane solution

    Boosted black brane solution


An introduction to the gravity fluid correspondence and its applications

Perturbative black brane solution

Boundary stress tensor (asymptotical AdS5)

Stress tensor of the dual fluid on the boundary


B the first order hydrodynamics via gravity fluid correspondence in the gauss bonnet gravity

B. The first order hydrodynamics via Gravity/Fluid correspondence in the Gauss-Bonnet gravity

1) G-B gravity

  • G-B gravity: action and equation


An introduction to the gravity fluid correspondence and its applications

2) Solution: 5-dimensional black brane


An introduction to the gravity fluid correspondence and its applications

3) Boosted black brane solution

: boundary coordinates

: boost velocities; constants

: projector onto spatial directions

: raise and lower the indices in boundary


An introduction to the gravity fluid correspondence and its applications

4) Perturbative solution (to first order)

  • : slowly varying functions of the boundary coordinates; expanded around

  • Correction terms needed

  • Coefficients of the first order correction terms


An introduction to the gravity fluid correspondence and its applications

  • Perturbative solution to the first order: around

  • Perturbative solution to the first order: global; covariant


An introduction to the gravity fluid correspondence and its applications

5) Boundary stress-tensor in the G-B gravity

  • Definition


An introduction to the gravity fluid correspondence and its applications

  • Explicit expression:

  • Non-zero components: Inserting global perturbative metric


An introduction to the gravity fluid correspondence and its applications

6) Stress tensor of the conformal field on the boundary

  • Background metric: the dual conformal filed

  • Expectation value of the stress tensor of the dual conformal field

  • Stress tensor of the dual theory

  • Pressure and viscosity


An introduction to the gravity fluid correspondence and its applications

7) Adding the Maxwell field

  • Action and solutions

  • Temperature and entropy density


An introduction to the gravity fluid correspondence and its applications

  • Solution in the Eddington-Finkelstin coordinate system

  • Solution in the boosted frame

    where

  • Perturbative solution: Similar as the case without Maxwell field;

    changed; New contents


An introduction to the gravity fluid correspondence and its applications

  • Stress tensor of the conformal field on the boundary

  • Conserved current of the conformal field on the boundary


C chern simons effects in gravity fluid correspondence

C. Chern-Simons effects in Gravity/Fluid correspondence

1) Maxwell Chern-Simons effect: anomalous magnetic and vortical effects (based on my two papers arXiv:1103.3773 Phys.Rev.D83:126003,2011 and arXiv:1112.4227)

  • G-B gravity with Maxwell Chern-simons: action and equations


An introduction to the gravity fluid correspondence and its applications

  • Black brane solution

  • Black brane Solution in the Eddington-Finkelstin coordinate


An introduction to the gravity fluid correspondence and its applications

  • Boosted black brane solution

    where

  • Perturbative solution


An introduction to the gravity fluid correspondence and its applications

Coefficients expressions


An introduction to the gravity fluid correspondence and its applications

  • Stress tensor of the dual fluid on the boundary

  • Charged current of the dual fluid on the boundary


An introduction to the gravity fluid correspondence and its applications

  • Notes:

    Anomalous magnetic and vortical effects:

    Charged current non-conserved: triangle anomalies

    New term: general case; physical or unphysical?

    The other special case:


D holographic charged fluid with anomalous current at finite cutoff surface

D. Holographic charged fluid with anomalous current at finite cutoffsurface

1) Einstein-Maxwell gravity with Chern-Simons term

2) RN-AdS black brane solution


An introduction to the gravity fluid correspondence and its applications

3) RN-AdS black brane solution in Eddington-Finkelstin coordinate system

New Coordinate Transformation:


An introduction to the gravity fluid correspondence and its applications

4) Boosted RN-AdS black brane solution

: boundary coordinates

: boost velocities; constants

: projector onto spatial directions

: raise and lower the indices in boundary


An introduction to the gravity fluid correspondence and its applications

5) Perturbative solution (to first order)

6) The stress tensor and Charged current of dual fluid


An introduction to the gravity fluid correspondence and its applications

7) Coefficients

Fixed by considering three conditions:


An introduction to the gravity fluid correspondence and its applications

8)Final expressions of the stress tensor and charged current of dual fluid at finite cutoff surface


E conclusion and discussion

E. Conclusion and discussion

1) Gravity/Fluid correspondence: long wavelength limit in

AdS/CFT correspondence

2) Fundamental algorithm and procedure in Gravity/Fluid

correspondence

3) Indeed deduce conformal viscous fluid in G-B gravity

4) The ratio of viscosity to entropy density: same as

other methods

5) Entropy density: same as black brane solution

6) Considering Maxwell field in the bulk: dual charged current

in the boundary


An introduction to the gravity fluid correspondence and its applications

7) Chern-Simons effects in Gravity/Fluid correspondence:

Anomalous magnetic and vortical effects;

Hall viscosity;

………

8) The anomalous magnetic and vortical effects

9) New term physical or unphysical?

10) Underlying relation between Topological insulator in

condensate matter and Chern-Simons term?

(PRB78,195424,2008)


An introduction to the gravity fluid correspondence and its applications

11) Near the infinite boundary case: large

12) Entropy density and thermodynamic relations


An introduction to the gravity fluid correspondence and its applications

13) The anomalous coefficients at the cutoff surface:

Comparison at the infinite boundary surface:

14) Non-conformal fluid, zero bulk viscosity?


Thanks

Thanks!


  • Login