An engineer's approach to AdS/CFT: Tutorial on computing real-time thermal Green's functions

by Matthias Kaminski

In the context of this KITP workshop on AdS/CMT, I have demonstrated how to compute real-time thermal Green's functions in a small tutorial. This page contains references which we have been using, or which I find useful. There are also two notebooks, one showing the computation for a bosonic example, the other for a fermionic one.

DISCLAIMER: Please note that the references are often not the original ones (not the ones who did it first) but whose presentation I like.

REFERENCES

1. The real-time response recipe and bosonic examples: a) Derivation in section II of [Iqbal,Liu'09].

b) Step by step calculation of exact solution for <J^m J^n> (charge current correlators) in hydrodynamic limit in section 3.1.2 of [Kaminski'08]

c) Example of the <T^{xy}T^{xy}> (energy-momentum tensor correlators) in section 6.1 of [Policastro,Son,Starinets'02].

d) Summary of numerical methods (including the one we used) in section 3.1.3 of [Kaminski'08].

2. Recipe for fermions and examples: a) Derivation in section III of [Iqbal,Liu'09].

b) Dirac equation in the conventions that are used in the notebook is given in (41) and (42) of [Benini et al'10].

c) General properties of fermionic Green's functions, and sum rules (plus description of the recipe for fermions) in section 5 of [Gulotta,Herzog,Kaminski'10].

d) Very detailed discussion of the example of fermions in AdS4 in section 2.1 of [Ammon et al'10].

3. Additional material a) Discussion of various boundary conditions for bulk fields (this allows also dynamical gauge fields on the boundary) in [Marolf,Ross'06].

b) Recent lecture notes by Nabil Iqbal, Hong Liu and Mark Mezei on Holographic (Non-) Fermi liquids [Iqbal,Liu,Mezei'11].

## Table of Contents

Here's a page to share important papers, review articles, relevant news, etc.

## Link to reference page from 2009 miniprogram Quantum Criticality and the AdS/CFT Correspondence.

## Black Hole Entropy and intermediate-temperature states of matter

## References for J. McGreevy's talk.

some black hole thermodynamics refs:Jacobsen

Townsend

black hole information problem:

Susskind and Lindesay

Bigatti and Susskind

BH information problem in AdS and information restoration at finite N:

Maldacena

Barbon and Rabinovici

Barbon and Rabinovici

Kleban et al

Festuccia and Liu

Iizuka and Polchinski

Iizuka, Okuda, Polchinski

Holographic Fermi surfaces:

Faulkner et al

Matching calculation

Another z=\infty strange metal:

Sachdev

A viewpoint on this.

Spin-incoherent Luttinger liquid

An engineer's approach to AdS/CFT: Tutorial on computing real-time thermal Green's functionsby Matthias KaminskiIn the context of this KITP workshop on AdS/CMT, I have demonstrated how to compute real-time thermal Green's functions in a small tutorial. This page contains references which we have been using, or which I find useful.

There are also two notebooks, one showing the computation for a bosonic example, the other for a fermionic one.

DISCLAIMER:Please note that the references are often not the original ones (not the ones who did it first) but whose presentation I like.REFERENCESa) Derivation in section II of

[Iqbal,Liu'09].

b) Step by step calculation of exact solution for <J^m J^n> (charge current correlators) in hydrodynamic limit in section 3.1.2 of

[Kaminski'08]

c) Example of the <T^{xy}T^{xy}> (energy-momentum tensor correlators) in section 6.1 of

[Policastro,Son,Starinets'02].

d) Summary of numerical methods (including the one we used) in section 3.1.3 of

[Kaminski'08].

2. Recipe for fermions and examples:

a) Derivation in section III of

[Iqbal,Liu'09].

b) Dirac equation in the conventions that are used in the notebook is given in (41) and (42) of

[Benini et al'10].

c) General properties of fermionic Green's functions, and sum rules (plus description of the recipe for fermions) in section 5 of

[Gulotta,Herzog,Kaminski'10].

d) Very detailed discussion of the example of fermions in AdS4 in section 2.1 of

[Ammon et al'10].

e) Two of the original references

[Liu,McGreevy,Vegh'09],

[Faulkner et al'09].

3. Additional material

a) Discussion of various boundary conditions for bulk fields (this allows also dynamical gauge fields on the boundary) in

[Marolf,Ross'06].

b) Recent lecture notes by Nabil Iqbal, Hong Liu and Mark Mezei on Holographic (Non-) Fermi liquids

[Iqbal,Liu,Mezei'11].

NOTEBOOKS(ii) Fermionic example