# Critical point in a holographic defect field theory

## TL;DR

This paper investigates a holographic gauge theory with a defect, revealing a second order phase transition at finite temperature characterized by diverging second derivatives of free energy and critical exponents.

## Contribution

It introduces a holographic model with a domain wall and non-commutative scalars, analyzing critical behavior and phase transition properties.

## Key findings

- Identifies a second order phase transition at finite temperature.
- Calculates critical exponents of -2/3 for free energy derivatives.
- Shows the presence of a domain wall separating different gauge group ranks.

## Abstract

We study a holographic gauge theory dual to the D3/D5 intersection. We consider a pure gauge B-field flux through the internal two-sphere wrapped by the probe D5--brane, which corresponds to a non-commutative configuration of adjoint scalars. There is a domain wall separating the theory into regions with different ranks of the adjoint group. At zero temperature the theory is supersymmetric and at finite temperature there is a critical point of a second order phase transition. We study the corresponding critical exponents and find that the second derivatives of the free energy, with respect to the bare mass and the magnetic field, diverge with a critical exponent of -2/3.