Quantization and variational problem of the Gubser-Rocha Einstein-Maxwell-Dilaton model, conformal and non-conformal deformations, and its proper thermodynamics

TL;DR

This paper explores the holographic dual of the Gubser-Rocha Einstein-Maxwell-Dilaton model, revealing a family of solutions representing a local quantum critical phase rather than a single IR fixed point, with implications for thermodynamics and operator interpretations.

Contribution

It demonstrates that the Gubser-Rocha model corresponds to a one-parameter family of solutions, not just a single IR fixed point, and analyzes their thermodynamic and holographic properties.

Findings

The dual field theory describes a local quantum critical phase.

Multiple solutions exist with different scalar charges and interpretations.

The analytic black hole is a special case within a broader solution space.

Abstract

We show that the strongly coupled field theory holographically dual to the Gubser-Rocha anti-de-Sitter Einstein-Maxwell-Dilaton theory describes not a single non-trivial AdS$_2$ IR fixed point, but a one-parameter family. It is dual to a local quantum critical phase instead of a quantum critical point. This result follows from a detailed analysis of the possible quantizations of the gravitational theory that is consistent with the thermodynamics of the analytical Gubser-Rocha black hole solution. The analytic Gubser-Rocha black hole is only a 2-parameter subset of all possible solutions, and we construct other members numerically. These new numerical solutions correspond to turning on an additional scalar charge. Moreover, each solution has multiple holographic interpretations depending on the quantization chosen. In one particular quantization involving a multitrace deformation the scalar charge is a marginal operator. In other quantizations where the marginal multitrace operator is turned off, the analytic Gubser-Rocha black hole does not describe a finite temperature conformal fluid.