We show that adjoint QCD features very strong Bose-Fermi cancellations in the large-N limit, despite the fact that it is manifestly nonsupersymmetric. The difference between the bosonic and fermionic densities of states in large-N adjoint QCD turns out to have a "two-dimensional" scaling ∼exp(E) for large energies E in finite spatial volume, where is a length scale associated with the curvature of the spatial manifold. In particular, all Hagedorn growth cancels, and so does the growth exp(V1/4E3/4) expected in a standard local four-dimensional theory in spatial volume V. In these ways, large-N adjoint QCD, a manifestly nonsupersymmetric theory, acts similarly to supersymmetric theories. We also show that at large-N the vacuum energy of multiflavor adjoint QCD is non-negative and exponentially small compared to the UV cutoff with several natural regulators.
Bibliographical noteFunding Information:
We are very grateful to Keith Dienes, Patrick Draper, Zohar Komargodski, and David McGady for helpful comments and are especially indebted to Larry Yaffe for a crucial suggestion on our analysis and extensive discussion concerning holonomy effective potentials. This work was supported in part by the DOE Grant No. DE-sc0011842 and by the National Science Foundation under Grant No. NSF PHY17-48958, and we are grateful to Kavli Institute for Theoretical Physics for its hospitality during the early stages of this work. M. Ü. acknowledges support from U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award No. DE-FG02-03ER41260.
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