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arXiv · 2111.04725

Universal fine grained asymptotics of free and weakly coupled Quantum Field Theory

Weiguang Cao·Tom Melia·Sridip Pal
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Abstract

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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Weiguang Cao, Tom Melia, Sridip Pal. 2021-11-08. Universal fine grained asymptotics of free and weakly coupled Quantum Field Theory. https://arxiv.org/abs/2111.04725

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