Harmonic analysis of 2d CFT partition functions
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
- Eprint ID
- 111588
- Resolver ID
- CaltechAUTHORS:20211021-204222884
- 488653
- Simons Foundation
- DE-SC0015845
- Department of Energy (DOE)
- Alfred P. Sloan Foundation
- 385602
- Simons Foundation
- SAPIN-2020-00047
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Ministry of Education, Culture, Sports, Science and Technology (MEXT)
- DE-SC0011632
- Department of Energy (DOE)
- 853507
- European Research Council (ERC)
- SCOAP3
- Created
-
2021-10-22Created from EPrint's datestamp field
- Updated
-
2021-10-26Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics