Phase transition and hyperscaling violation for scalar Black Branes

TL;DR

This paper explores the thermodynamics and scaling symmetries of scalar black brane solutions in Einstein-scalar gravity, revealing phase transitions and hyperscaling violation properties relevant to boundary field theories.

Contribution

It demonstrates the emergence of hyperscaling violation and phase transitions in scalar black branes, extending understanding beyond specific models to more general Einstein-scalar theories.

Findings

Scalar black branes exhibit hyperscaling violation with negative parameter.

A phase transition occurs at a critical temperature favoring scalar-dressed solutions.

The model's features are generic for Einstein-scalar gravity with positive scalar mass squared.

Abstract

We investigate the thermodynamical behavior and the scaling symmetries of the scalar dressed black brane (BB) solutions of a recently proposed, exactly integrable Einstein-scalar gravity model [1], which also arises as compactification of (p-1)-branes with a smeared charge. The extremal, zero temperature, solution is a scalar soliton interpolating between a conformal invariant AdS vacuum in the near-horizon region and a scale covariant metric (generating hyperscaling violation on the boundary field theory) asymptotically. We show explicitly that for the boundary field theory this implies the emergence of an UV length scale (related to the size of the brane), which decouples in the IR, where conformal invariance is restored. We also show that at high temperatures the system undergoes a phase transition. Whereas at small temperature the Schwarzschild-AdS BB is stable, above a critical temperature the scale covariant, scalar-dressed BB solution, becomes energetically preferred. We calculate the critical exponent z and the hyperscaling violation parameter of the scalar-dressed phase. In particular we show that the hyperscaling violation parameter is always negative. We also show that the above features are not a peculiarity of the exact integrable model of Ref.[1], but are a quite generic feature of Einstein-scalar and Einstein-Maxwell-scalar gravity models for which the squared-mass of the scalar field is positive and the potential vanishes exponentially as the scalar field goes to minus infinity.