Harmonic analysis of 2d CFT partition functions

• Published in: The journal of high energy physics Vol. 2021; no. 9; pp. 1 - 51
• Main Authors: Benjamin, Nathan, Collier, Scott, Fitzpatrick, A. Liam, Maloney, Alexander, Perlmutter, Eric
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 27.09.2021; Springer Nature B.V; Springer; Springer Nature; SpringerOpen
• Subjects: Bosons; Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Conformal and W Symmetry; Conformal Field Theory; Decomposition; Eigenvectors; Elementary Particles; Field Theories in Lower Dimensions; Fourier analysis; Harmonic analysis; High energy physics; High Energy Physics - Theory; Operators (mathematics); Partitions (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Spectral theory; String Theory; Field Theories in Lower Dimensions; Conformal Field Theory; Conformal and W Symmetry; spectral; operator: local; moduli space; dimension: 2; analysis: harmonic; operator: spectrum; field theory: conformal; anti-de Sitter; gravitation; partition function; SL; Z
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP09(2021)174

A bstract 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.