# Universality of Holographic Phase Transitions and Holographic Quantum Liquids

## TL;DR

This paper investigates the phase transitions in holographic gauge theories with defects, revealing two universality classes characterized by different phase transition orders, and explores their dependence on defect codimension and other parameters.

## Contribution

It identifies two universality classes of phase transitions in holographic defect theories based on the order of the transition, linked to the defect's codimension.

## Key findings

- Systems without defects exhibit third order phase transitions.
- Defect theories with (p-1)-spatial directions show second order phase transitions.
- A thermodynamical instability appears at low temperature for p<3.

## Abstract

We explore the phase structure for defect theories in full generality using the gauge/gravity correspondence. On the gravity side, the systems are constructed by introducing M (probe) D(p+4-2k)-branes in a background generated by N Dp-branes to obtain a codimension-k intersection. The dual gauge theory is a U(N) Supersymmetric Yang-Mills theory on a (1+p-k)-dimensional defect with both adjoint and fundamental degrees of freedom. We focus on the phase structure in the chemical potential versus temperature plane. We observe the existence of two universality classes for holographic gauge theories, which are identified by the order of the phase transition in the interior of the chemical potential/temperature plane. Specifically, all the sensible systems with no defect show a third order phase transition. Gauge theories on a defect with (p-1)-spatial directions are instead characterised by a second order phase transition. One can therefore state that the order of this phase transition is intimately related to the codimensionality of the defect. We also discuss the massless hypermultiplet at low temperature, where a thermodynamical instability seems to appear for $p<3$. Finally, we comment on such an instability.