Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 11, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP11(2020)134
Keywords
Conformal and W Symmetry; Conformal Field Theory; Field Theories in Lower Dimensions
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Funding
- European Research Council (ERC) under European Union [787185]
- European Research Council (ERC) [787185] Funding Source: European Research Council (ERC)
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A classical result from analytic number theory by Rademacher gives an exact formula for the Fourier coefficients of modular forms of non-positive weight. We apply similar techniques to study the spectrum of two-dimensional unitary conformal field theories, with no extended chiral algebra and c > 1. By exploiting the full modular constraints of the partition function we propose an expression for the spectral density in terms of the light spectrum of the theory. The expression is given in terms of a Rademacher expansion, which converges for spin j not equal 0. For a finite number of light operators the expression agrees with a variant of the Poincare construction developed by Maloney, Witten and Keller. With this framework we study the presence of negative density of states in the partition function dual to pure gravity, and propose a scenario to cure this negativity.
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