Universal fine grained asymptotics of free and weakly coupled quantum field theory

Creators: Cao, Weiguang^{1, 2}; Melia, Tom²; Pal, Sridip^{3, 4}

1. University of Tokyo
2. Kavli Institute for the Physics and Mathematics of the Universe
3. Institute for Advanced Study
4. California Institute of Technology

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Abstract

We give a rigorous proof that in any free quantum field theory with a finite group global symmetry G, on a compact spatial manifold, at sufficiently high energy, the density of states ρ_α(E) for each irreducible representation α of 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 G, where we prove a universal, albeit different, behavior.

Copyright and License

© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Article funded by SCOAP3.

Acknowledgement

W. C. is supported by the Global Science Graduate Course (GSGC) program of the University of Tokyo, the World Premier International Research Center Initiative (WPI) and acknowledges support from JSPS KAKENHI grant number JP19H05810, JP22J21553 and JP22KJ1072. T. M. is supported by the World Premier International Research Center Initiative (WPI) MEXT, Japan, and by JSPS KAKENHI grants JP18K13533, JP19H05810, JP20H01896, and JP20H00153. S. P. acknowledges funding provided by Tomislav and Vesna Kundic as well as the support from DOE grant DE-SC0009988. We thank D. Harlow and H. Ooguri for valuable comments and feedback on the draft. S. P. thanks D. Mazáč for teaching him amusing facts about group theory, G. J. Turiaci for an insightful journal club talk on [17] and J. Magan for explaining his proof of the conjecture.

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