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.
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Benjamin, N., Collier, S., Fitzpatrick, A.L. et al. Harmonic analysis of 2d CFT partition functions. J. High Energ. Phys. 2021, 174 (2021). https://doi.org/10.1007/JHEP09(2021)174
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DOI: https://doi.org/10.1007/JHEP09(2021)174