Deformations of Lifshitz holography with the Gauss-Bonnet term in ($n+1$) dimensions

TL;DR

This paper studies how Gauss-Bonnet corrections affect Lifshitz holography in higher dimensions, focusing on marginal deformations, critical exponents, and black hole thermodynamics.

Contribution

It introduces a framework for analyzing marginally relevant deformations in Gauss-Bonnet-Lifshitz holography across dimensions, deriving restrictions on the critical exponent and exploring black hole solutions.

Findings

Critical exponent z is restricted by z= n-1-2(n-2) te1lpha.

Black hole solutions characterized by horizon flux and Gauss-Bonnet coupling.

Thermodynamic properties depend on dimension n and coupling e1le1pha.

Abstract

We investigate deformations of Gauss-Bonnet-Lifshitz holography in $(n+1)$ dimensional spacetime. Marginally relevant operators are dynamically generated by a momentum scale $\Lambda \sim 0$ and correspond to slightly deformed Gauss-Bonnet-Lifshitz spacetimes via a holographic picture. To admit (non-trivial) sub-leading orders of the asymptotic solution for the marginal mode, we find that the value of the dynamical critical exponent $z$ is restricted by $z= n-1-2(n-2) \tilde{\alpha}$, where $\tilde{\alpha}$ is the (rescaled) Gauss-Bonnet coupling constant. The generic black hole solution, which is characterized by the horizon flux of the vector field and $\tilde{\alpha}$, is obtained in the bulk, and we explore its thermodynamic properties for various values of $n$ and $\tilde{\alpha}$.