Holographic Renormalization of Einstein-Maxwell-Dilaton Theories

TL;DR

This paper extends the boundary value problem framework in Einstein-Maxwell-Dilaton theories to include mixed boundary conditions involving gauge and scalar fields, revealing implications for dual operators and non-Fermi liquid behavior.

Contribution

It introduces a generalized boundary value problem with mixed conditions for gauge and scalar fields in Einstein-Maxwell-Dilaton theories, highlighting new boundary term effects.

Findings

Boundary conditions relate scalar and current operator expectation values.

Finite boundary terms affect physical quantities like mass in scalar theories.

The framework applies to non-Fermi liquid properties in fixed charge ensembles.

Abstract

We generalize the boundary value problem with a mixed boundary condition that involves the gauge and scalar fields in the context of Einstein-Maxwell-Dilaton theories. In particular, the expectation value of the dual scalar operator can be a function of the expectation value of the current operator. The properties are prevalent in a fixed charge ensemble because the conserved charge is shared by both fields through the dilaton coupling, which is also responsible for non-Fermi liquid properties. We study the on-shell action and the stress energy tensor to note practical importances of the boundary value problem. In the presence of the scalar fields, physical quantities are not fully fixed due to the finite boundary terms that manifest in the massless scalar or the scalar with mass saturating the Breitenlohner-Freedman bound.