Lifshitz holography with a probe Yang-Mills field

TL;DR

This paper investigates Lifshitz holography with a probe SU(2) Yang-Mills field in black hole backgrounds, analyzing phase transitions and critical behavior at finite temperature for different anisotropic scaling exponents.

Contribution

It introduces analytical and numerical methods to study phase transitions in Lifshitz holography with varying anisotropic scaling exponent z.

Findings

Determined critical temperature dependence on z

Identified phase transition characteristics

Provided analytical approximation for critical exponents

Abstract

Taking as a probe an SU(2) gauge field with Yang-Mills action in a 3+1 dimensional Lifshitz black hole background, we use the gauge/gravity correspondence to discuss finite temperature effects in the dual theory defined on the boundary. In order to test the dependence of results on the anisotropic scaling exponent z we consider two analytical black hole solutions with z=2 and z=4. Apart from solving the equations of motion in the bulk using a numerical approach, we also apply an analytical approximation allowing the determination of the phase transition character, the critical exponent and the critical temperature behavior as a function of z.