# Bose-Fermi cancellations without supersymmetry

## TL;DR

This paper demonstrates that large N adjoint QCD exhibits strong Bose-Fermi cancellations similar to supersymmetric theories, despite lacking supersymmetry, leading to suppressed density of states growth and small vacuum energy.

## Contribution

It reveals non-supersymmetric Bose-Fermi cancellations in large N adjoint QCD, showing suppressed state growth and small vacuum energy akin to supersymmetric theories.

## Key findings

- Bose-Fermi cancellations lead to two-dimensional scaling of density of states.
- Hagedorn growth and other exponential growths are canceled.
- Vacuum energy is non-negative and exponentially small at large N.

## 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.