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Harmonic analysis of 2d CFT partition functions
- Publication Year :
- 2021
-
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.<br />Comment: 35+24 pages, v2: corrected a mistake in Sec 3, v3: minor errors fixed
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2107.10744
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/JHEP09(2021)174