Metallic and antiferromagnetic fixed points from gravity

TL;DR

This paper investigates the RG flow of an SU(2)×U(1) gauge theory with adjoint matter, identifying fixed points corresponding to metallic and antiferromagnetic phases, and analyzing their stability conditions.

Contribution

It constructs the Callan-Symanzik equation and beta functions for the theory, revealing two distinct fixed points with different physical behaviors.

Findings

Identified metallic and antiferromagnetic fixed points.

Metallic phase becomes unstable under certain parameters.

Provided a detailed RG flow analysis for the gauge theory.

Abstract

We consider SU(2)$\times$ U(1) gauge theory coupled to matter field in adjoints and study RG group flow. We constructed Callan Symanzik equation and subsequent $\beta$ functions and study the fixed points. We find there are two fixed points, showing metallic and antiferromagnetic behaviour. We have shown that metallic phase develops an instability if certain parametric conditions are satisfied.