# Finite-Temperature Fractional D2-Branes and the Deconfinement Transition in 2+1 Dimensions

## TL;DR

This paper constructs a finite-temperature black-hole solution in supergravity dual to fractional D2-branes, revealing a first-order deconfinement transition in a 2+1 dimensional supersymmetric gauge theory.

## Contribution

It introduces a new regular horizon solution for fractional D2-branes, modeling the deconfined phase and transition in the dual gauge theory.

## Key findings

- Existence of a regular black-hole solution at finite temperature.
- Identification of a first-order deconfinement transition.
- Connections established to Chern--Simons theories and M2-branes.

## Abstract

The supergravity dual to N regular and M fractional D2-branes on the cone over \mathbb{CP}^3 has a naked singularity in the infrared. One can resolve this singularity and obtain a regular fractional D2-brane solution dual to a confining 2+1 dimensional N = 1 supersymmetric field theory. The confining vacuum of this theory is described by the solution of Cvetic, Gibbons, Lu and Pope. In this paper, we explore the alternative possibility for resolving the singularity - the creation of a regular horizon. The black-hole solution we find corresponds to the deconfined phase of this dual gauge theory in three dimensions. This solution is derived in perturbation theory in the number of fractional branes. We argue that there is a first-order deconfinement transition. Connections to Chern--Simons matter theories, the ABJM proposal and fractional M2-branes are presented.