Kavli Affiliate: Tom Melia
| First 5 Authors: Weiguang Cao, Tom Melia, Sridip Pal, ,
| Summary:
We give a rigorous proof that in any free 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. We further prove that this continues to
hold in a weakly coupled quantum field theory, given an appropriate scaling of
the coupling with temperature. This generalizes similar results that were
previously obtained in $(1+1)$-D to higher spacetime dimension. We discuss the
role of averaging in the density of states, and we compare and contrast with
the case of continuous group $mathrm{G}$, where we prove a universal, albeit
different, behavior.
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