Journal article
Rademacher expansions and the spectrum of 2d CFT
- Abstract:
- 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 ≠ 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Version of record, 629.8KB, Terms of use)
-
- Publisher copy:
- 10.1007/jhep11(2020)134
Authors
- Publisher:
- Springer
- Journal:
- Journal of High Energy Physics More from this journal
- Volume:
- 2020
- Issue:
- 11
- Article number:
- 134
- Publication date:
- 2020-11-25
- Acceptance date:
- 2020-10-19
- DOI:
- EISSN:
-
1029-8479
- ISSN:
-
1126-6708
- Language:
-
English
- Keywords:
- Pubs id:
-
1146964
- Local pid:
-
pubs:1146964
- Deposit date:
-
2020-11-27
Terms of use
- Copyright holder:
- Alday and Bae.
- Copyright date:
- 2020
- Rights statement:
- © The Authors. Article funded by SCOAP3. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- Licence:
- CC Attribution (CC BY)
If you are the owner of this record, you can report an update to it here: Report update to this record