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Published September 2021 | Version Accepted Version + Published
Journal Article Open

Harmonic analysis of 2d CFT partition functions

Creators

  • 1. ROR icon Princeton University
  • 2. ROR icon Boston University
  • 3. ROR icon McGill University
  • 4. ROR icon L'Institut de physique théorique
  • 5. ROR icon California Institute of Technology

Abstract

We apply the theory of harmonic analysis on the fundamental domain of SL(2, ℤ) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space ℍ/SL(2, ℤ), and of target space moduli space O(c, c; ℤ)\O(c, c; ℝ)/O(c)×O(c). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.

Additional Information

© 2021 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. Received: August 17, 2021; Accepted: September 8, 2021; Published: September 27, 2021. We are grateful to Fernando Alday, Tolya Dymarsky, Tom Hartman, Jeff Harvey, Peter Humphries, Yuya Kusuki, Ying-Hsuan Lin, Hirosi Ooguri, Boris Pioline, Sylvain Ribault, Steve Shenker, Andrew Sutherland, Yifan Wang, Xinan Zhou, and especially Herman Verlinde for very helpful discussions. NB is supported in part by the Simons Foundation Grant No. 488653. ALF is supported by the US Department of Energy Office of Science under Award Number DE-SC0015845, the Simons Collaboration on the Non-Perturbative Bootstrap, and a Sloan Foundation fellowship. AM is supported by the Simons Foundation Grant No. 385602 and the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number SAPIN-2020-00047. EP is supported by the World Premier International Research Center Initiative, MEXT, Japan, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by ERC Starting Grant 853507.

Attached Files

Published - Benjamin2021_Article_HarmonicAnalysisOf2dCFTPartiti.pdf

Accepted Version - 2107.10744.pdf

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Additional details

Identifiers

Eprint ID
111588
Resolver ID
CaltechAUTHORS:20211021-204222884

Related works

Describes
https://arxiv.org/abs/2107.10744 (URL)

Funding

Simons Foundation
488653
Department of Energy (DOE)
DE-SC0015845
Alfred P. Sloan Foundation
Simons Foundation
385602
Natural Sciences and Engineering Research Council of Canada (NSERC)
SAPIN-2020-00047
Ministry of Education, Culture, Sports, Science and Technology (MEXT)
Department of Energy (DOE)
DE-SC0011632
European Research Council (ERC)
853507
SCOAP3

Dates

Created
2021-10-22
Created from EPrint's datestamp field
Updated
2021-10-26
Created from EPrint's last_modified field

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Caltech groups
Walter Burke Institute for Theoretical Physics