Bose-Fermi cancellations without supersymmetry

Abstract

We show that adjoint QCD features very strong Bose-Fermi cancellations in the large $N$ limit, despite the fact that it is manifestly non-supersymmetric. The difference between the bosonic and fermionic densities of states in large $N$ adjoint QCD turns out to have a `two-dimensional' scaling $\sim \exp (\sqrt{\ell E})$ for large energies $E$ in finite spatial volume, where $\ell$ is a length scale associated with the curvature of the spatial manifold. In particular, all Hagedorn growth cancels, and so does the growth $\exp (V^{1/4}{E}^{3/4})$ expected in a standard local 4d theory in spatial volume $V$. In these ways, large $N$ adjoint QCD, a manifestly non-supersymmetric theory, acts similarly to supersymmetric theories. We also show that at large $N$, the vacuum energy of multi-flavor adjoint QCD is non-negative and exponentially small compared to the UV cutoff with several natural regulators.

v2: fixed small typos, small improvements to exposition, and added an appendix. Improved title to better reflect content

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Cited by in corpus (10)

• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• Generalized 't Hooft anomalies on non-spin manifolds
• A possible phase for adjoint QCD
• Quantum distillation in QCD
• Renormalons beyond the Borel plane
• Densities of States and the CKN Bound
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories
• Supersymmetric Proximity