# Towards a Holographic Model of Color-Flavor Locking Phase

## TL;DR

This paper constructs a holographic model of the color-flavor locking phase using D-brane configurations in string theory, showing how baryon density influences symmetry breaking and phase structure at finite temperature.

## Contribution

It introduces a holographic realization of the color-flavor locking phase with a detailed analysis of baryonic effects and temperature dependence in a string theory framework.

## Key findings

- Baryonic density induces a potential that dissolves instantons on D7-branes.
- Color-flavor locking persists at finite temperature.
- Thermal effects modify the phase diagram and symmetry breaking patterns.

## Abstract

We demonstrate a holographic realization of color-flavor locking phase, using N=4 SU(Nc) SYM coupled to N=2 Nf fundamental hypermultiplets as an example. The gravity dual consists of Nc D3-branes and Nf D7-branes with world volume gauge field representing the baryon density. Treating a small number \tilde{N}c << Nc of D3-branes as Yang-Mills instantons on the D7-branes, we consider possible potential(s) on their moduli space or equivalently the Higgs branch. We show that a non-trivial potential can be generated by including the backreaction of the baryonic density on the D7-branes, this dynamically drives the instantons (= D3-branes) into dissolution. We interpret this as a color-flavor locking since the size of the instanton is the squark vev, and study the symmetry breaking patterns. Extending to finite temperature setup, we demonstrate that color-flavor locking persists, and the thermal effect provides additional structures in the phase diagram.