Kavli Affiliate: Tom Melia
| First 5 Authors: Weiguang Cao, Tom Melia, Sridip Pal, ,
| Summary:
We give a proof that in any weakly coupled quantum field theory with a finite
group global symmetry $mathrm{G}$, on a compact spatial manifold, at
sufficiently high energy, the density of states $rho_alpha(E)$ for each
irreducible representation $alpha$ of $mathrm{G}$ obeys a universal formula
as conjectured by Harlow and Ooguri. This generalizes similar results that were
previously obtained in $(1+1)$-D to higher spacetime dimension. The basic idea
of the proof relies on the approximate existence of a Hilbert series in the
weakly coupled regime, and is also applicable to the calculation of twisted
supersymmetric indices. We further compare and contrast with the scenario of
continuous $mathrm{G}$, where we prove a universal, albeit different,
behavior. We discuss the role of averaging in the density of states.
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