Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 9, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP09(2021)174
Keywords
Conformal and W Symmetry; Conformal Field Theory; Field Theories in Lower Dimensions
Categories
Funding
- Simons Foundation [488653, 385602]
- US Department of Energy Office of Scienceunder [DE-SC0015845]
- Simons Collaboration on the NonPerturbative Bootstrap
- Sloan Foundation fellowship
- Natural Sciences and Engineering Research Council of Canada (NSERC) [SAPIN-2020-00047]
- World Premier International Research Center Initiative, MEXT, Japan
- U.S. Department of Energy, Office of Science, Office of High Energy Physics [DE-SC0011632]
- ERC Starting [853507]
- European Research Council (ERC) [853507] Funding Source: European Research Council (ERC)
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The text discusses the application of harmonic analysis theory to study the partition functions of two-dimensional conformal field theories, decomposing them into eigenfunctions of different moduli spaces and exploring their relevance to AdS(3) gravity. It emphasizes that the local operator spectrum is fully determined by a specific subset of degeneracies.
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)xO(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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