The 2-loop partition function of large N gauge theories with adjoint matter on S^3

TL;DR

This paper calculates the 2-loop thermal partition function of large N Yang-Mills theory with adjoint matter on a small 3-sphere, providing insights into spectral corrections and phase transition behavior at weak coupling.

Contribution

It presents the first 2-loop computation of the partition function for this class of theories, including scalars and fermions with arbitrary couplings, advancing understanding of deconfinement transitions.

Findings

Perturbative corrections to the spectrum are derived.

The Hagedorn temperature correction is obtained.

Lays groundwork for 3-loop phase transition analysis.

Abstract

We compute the 2-loop thermal partition function of Yang-Mills theory on a small 3-sphere, in the large N limit with weak 't Hooft coupling. We include N_s scalars and N_f chiral fermions in the adjoint representation of the gauge group (S)U(N), with arbitrary Yukawa and quartic scalar couplings, assuming only commutator interactions. From this computation one can extract information on the perturbative corrections to the spectrum of the theory, and the correction to its Hagedorn temperature. Furthermore, the computation of the 2-loop partition function is a necessary step towards determining the order of the deconfinement phase transition at weak coupling, for which a 3-loop computation is needed.