# Color Superconductivity in Holographic SYM Theory

## TL;DR

This paper investigates the existence of color superconductivity in supersymmetric Yang-Mills theory using a holographic model, finding that the phase appears in probe approximation but vanishes when back-reaction is included.

## Contribution

It introduces a holographic bottom-up model to study color superconductivity in supersymmetric Yang-Mills theory and examines the effects of back-reaction on the phase structure.

## Key findings

- Color superconductivity appears in the probe approximation above a critical chemical potential.
- Including back-reaction causes the superconducting phase to disappear.
- The results suggest the superconducting phase is sensitive to the model's parameters and approximations.

## Abstract

A holographic bottom-up model used in studying the superconducting system is applied to search for the color superconducting phase of supersymmetric Yang-Mills theory. We apply the probe analysis of this model to the supersymmetric Yang-Mills theory in both the confinement and deconfinement phases. In this analysis, we find the color superconductivity in both phases when the baryon chemical potential exceeds a certain critical value. This result implies that, above the critical chemical potential, a color non-singlet diquark operator, namely the Cooper pair, has its vacuum expectation value even in the confinement phase. In order to improve this peculiar situation, we proceed the analysis by taking account of the full back-reaction from the probe. As a result, the color superconducting phase, which is observed in the probe approximation, disappears in both the confinement and deconfinement phases when parameters of the theory are set within their reasonable values.