Bose-Fermi degeneracies in large N adjoint QCD

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 S³ × S¹. We focus on the weakly-coupled confining small-S³ regime. If the fermions are given periodic boundary conditions on S¹, 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 S¹ 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 ∼ N⁰, 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.