Harmonic analysis of 2d CFT partition functions
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Published version
Date
2021-09
Authors
Benjamin, Nathan
Collier, Scott
Fitzpatrick, A. Liam
Maloney, Alexander
Perlmutter, Eric
Version
OA Version
Citation
N. Benjamin, S. Collier, A.L. Fitzpatrick, A. Maloney, E. Perlmutter. 2021. "Harmonic analysis of 2d CFT partition functions." Journal of High Energy Physics, Volume 2021, Issue 9, https://doi.org/10.1007/jhep09(2021)174
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 AdS_3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.
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Copyright The Authors. Open Access . 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.