Benjamin, NathanCollier, ScottFitzpatrick, A. LiamMaloney, AlexanderPerlmutter, Eric2022-06-202022-06-202021-09N. 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)1741029-8479https://hdl.handle.net/2144/44751We 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.en-USCopyright 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.http://creativecommons.org/licenses/by/4.0/Article10.1007/jhep09(2021)174644038