A holographic model for hall viscosity

Jiunn-Wei Chen,Nien-En Lee,Debaprasad Maity,Wen-Yu Wen

doi:10.1016/j.physletb.2012.05.026

Jiunn-Wei Chen, Nien-En Lee + Show 2 more

Open Access

https://doi.org/10.1016/j.physletb.2012.05.026

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Abstract

We have modified the holographic model of Saremi and Son [12] by using a charged black brane, instead of a neutral one, such that when the bulk pseudo scalar (θ) potential is made of θ2 and θ4 terms, parity can still be broken spontaneously in the boundary theory. In our model, the 3+1 dimensional bulk has a pseudo scalar coupled to the gravitational Chern–Simons term in the anti de Sitter charged black brane back ground. Parity could be broken spontaneously in the bulk by the pseudo scalar hairy solution and give rise to non-zero Hall viscosity at the boundary theory.

Highlights

In recent years, the AdS/CFT correspondence [1,2,3] has been applied to study strongly coupled phenomena in condensed matter physics at finite temperature and chemical potential
Like the other transport coefficients, Hall viscosity is found to be uniquely determined by the near horizon data of the bulk black brane [12]
In the original construction the (3 + 1) dimensional bulk action has a negative cosmological constant, a real scalar field coupled to the gravitational Chern–Simons term

Summary

Introduction

The AdS/CFT correspondence [1,2,3] has been applied to study strongly coupled phenomena in condensed matter physics at finite temperature and chemical potential. Like the other transport coefficients, Hall viscosity is found to be uniquely determined by the near horizon data of the bulk black brane [12]. This is yet another example of the membrane paradigm. It has been shown that a neutral scalar hair with quadratic and quartic potential that satisfies the usual sourceless boundary condition in a Schwarzschild-AdS black hole spacetime does not satisfy the positive energy theorem [16]. The pseudo scalar hair, breaks parity spontaneously and gives a pseudo scalar condensate in the boundary field theory which, as we will demonstrate, is important for Hall viscosity. A detailed derivation of Hall viscosity together with an analytical approximation are given in Appendices A and B

General properties of viscosities

The action and equations of motion are invariant under the following scaling:

The Hall viscosity

Conclusion