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

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.

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• Phases of large $N$ vector Chern-Simons theories on $S^2\times S^1$
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• Duality and Higher Temperature Phases of Large $N$ Chern-Simons Matter Theories on $S^2\times S^1$
• Large $N$ phase transitions and the fate of small Schwarzschild-AdS black holes
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Spectral sum rules for confining large-N theories
• One-Loop Partition Functions in Deformed $\mathcal{N}=4$ SYM Theory
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• Constraints on the R-charges of Free Bound States from the Römelsberger Index
• Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories
• A hitchhiker's guide to quantum field theoretic aspects of $\mathcal{N}=4$ SYM theory and its deformations