Bose-Fermi Degeneracies in Large $N$ Adjoint QCD

TL;DR

This paper studies large N adjoint QCD on S^3 x S^1, revealing boson-fermion cancellations that prevent Hagedorn instabilities and support volume independence, despite the theory being non-supersymmetric at finite N.

Contribution

It demonstrates large N boson-fermion cancellations in adjoint QCD, explaining the absence of Hagedorn instabilities and supporting volume independence without supersymmetry.

Findings

Boson-fermion cancellations occur at large N in adjoint QCD.

No Hagedorn instabilities for any S^1 size L.

Adjoint QCD remains confining for all L, despite non-supersymmetry.

Abstract

We analyze the large $N$ limit of adjoint QCD, an $SU(N)$ gauge theory with $N_f$ flavors of massless adjoint Majorana fermions, compactified on $S^3 \times S^1$. We focus on the weakly-coupled confining small-$S^3$ regime. If the fermions are given periodic boundary conditions on $S^1$, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition function. These cancellations follow a pattern previously seen in the context of misaligned supersymmetry, and lead to the absence of Hagedorn instabilities for any $S^1$ size $L$, even though the bosonic and fermionic densities of states both have Hagedorn growth. Adjoint QCD stays in the confining phase for any $L \sim N^0$, explaining how it is able to enjoy large $N$ volume independence for any $L$. The large $N$ boson-fermion cancellations take place in a setting where adjoint QCD is manifestly non-supersymmetric at any finite $N$, and are consistent with the recent conjecture that adjoint QCD has emergent fermionic symmetries in the large $N$ limit.