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Harmonic analysis of 2d CFT partition functions

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arxiv 2107.10744 v3 pith:HJH7TEF6 submitted 2021-07-22 hep-th

Nathan Benjamin , Scott Collier , A. Liam Fitzpatrick , Alexander Maloney , Eric Perlmutter This is my paper · ORCID
classification hep-th
keywords mathbbpartitionanalysisfunctionsharmonicspacetheoriescertain
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abstract

We apply the theory of harmonic analysis on the fundamental domain of $SL(2,\mathbb{Z})$ 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 $\mathbb H/SL(2,\mathbb Z)$, and of target space moduli space $O(c,c;\mathbb Z)\backslash O(c,c;\mathbb R)/O(c)\times O(c)$. 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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Cited by 6 Pith papers

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