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.
Highlights
The goal of this paper is to discuss relations between bosonic and fermionic excitations in four-dimensional adjoint QCD
Despite the manifest lack of supersymmetry in adjoint QCD with nf > 1, these relations turn out to be surprisingly powerful. These relations turn out to be as powerful as the Bose-Fermi relations in supersymmetric quantum field theories (QFTs)
Introducing a ð−1ÞF grading makes adjoint QCD remain confining at small L, in the sense that center symmetry is not spontaneously broken
Summary
Despite the manifest lack of supersymmetry in adjoint QCD with nf > 1, these relations turn out to be surprisingly powerful In several ways, these relations turn out to be as powerful as the Bose-Fermi relations in supersymmetric QFTs. To probe relations between bosonic and fermionic states, we will mostly consider a ð−1ÞF-graded grand-canonical partition function ZðLÞ and the related grand-canonical ð−1ÞF-graded density of states ρðEÞ:. QFTs, on the other hand, one expects log ρðEÞ ∼ V1=4E3=4 no SUSY ⇒ log ZðLÞ ∼ V=L3: ð1:3Þ These scaling relations follow from the expectation that the partition function should have an extensive dependence on the spatial volume V in the absence of high-energy Bose-Fermi cancellations. We find that at small LΛ the graded partition function scales as log
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