Hyperscaling violation for scalar black branes in arbitrary dimensions

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.