Hyperscaling violation for scalar black branes in arbitrary dimensions

TL;DR

This paper generalizes hyperscaling violation and phase transition results to scalar black branes in arbitrary dimensions, deriving analytic solutions and analyzing their thermodynamics, correlators, and supergravity origins.

Contribution

It provides new analytic scalar black brane solutions in arbitrary dimensions, revealing their phase transitions, critical exponents, and relation to supergravity p-branes.

Findings

Identified phase transition between Schwarzschild-AdS and scalar-dressed black branes.

Calculated critical exponents and hyperscaling violation parameters.

Derived short-distance correlator behavior for scalar operators.

Abstract

We extend to black branes (BB) in arbitrary dimensions the results of Ref. [1] about hyperscaling violation and phase transition for scalar black 2-branes. We derive the analytic form of the (d+1)-dimensional scalar soliton interpolating between a conformal invariant AdS vacuum in the infrared and a scale covariant metric in the ultraviolet. We show that the thermodynamical system undergoes a phase transition between Schwarzschild-AdS and a scalar-dressed BB. We calculate the critical exponent and the hyperscaling violation parameter in the two phases. We show that our scalar BB solutions generically emerge as compactifications of p-brane solutions of supergravity theories. We also derive the short distance form of the correlators for the scalar operators corresponding to an UV exponential potential supporting our black brane solution. We show that also for negative values of the hyperscaling violation parameter these correlators have a short distance power-law behavior.