Shear sum rules at finite chemical potential

TL;DR

This paper derives shear sum rules at finite chemical potential for various gravitational duals, revealing additional terms due to scalar operators with non-trivial vacuum expectation values.

Contribution

It extends shear sum rules to finite chemical potential settings, incorporating effects of scalar operators in the operator product expansion.

Findings

Sum rules are derived for N=4 Yang-Mills, M2-branes, and M5-branes.

Additional terms involving chemical potential appear in the sum rules.

Scalar operators with non-trivial vacuum expectation values cause these modifications.

Abstract

We derive sum rules which constrain the spectral density corresponding to the retarded propagator of the T_{xy} component of the stress tensor for three gravitational duals. The shear sum rule is obtained for the gravitational dual of the N=4 Yang-Mills, theory of the M2-branes and M5-branes all at finite chemical potential. We show that at finite chemical potential there are additional terms in the sum rule which involve the chemical potential. These modifications are shown to be due to the presence of scalars in the operator product expansion of the stress tensor which have non-trivial vacuum expectation values at finite chemical potential.