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DOE OSTI · 1851504

Harmonic analysis of 2d CFT partition functions

Benjamin, Nathan·Collier, Scott·Fitzpatrick, A. Liam·Maloney, Alexander·Perlmutter, Eric
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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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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSConformal and W symmetryConformal field theoryField theories in lower dimensionsPhysics

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Benjamin, Nathan, Collier, Scott, Fitzpatrick, A. Liam, Maloney, Alexander, Perlmutter, Eric. 2021-09-27. Harmonic analysis of 2d CFT partition functions. https://doi.org/10.1007/jhep09(2021)174

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