$T\overline T$-deformed modular forms
| Autor: | Cardy, John |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Communications in Number Theory and Physics, Vol. 16, No. 3 (2022), pp. 435-457 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4310/CNTP.2022.v16.n3.a1 |
| Popis: | Certain objects of conformal field theory, for example partition functions on the rectangle and the torus, and one-point functions on the torus, are either invariant or transform simply under the modular group, properties which should be preserved under the $T\overline T$ deformation. The formulation and proof of this statement in fact extents to more general functions such as $T\overline T$ deformed modular and Jacobi forms. We show that the deformation acts simply on their Mellin transform, multiplying it by a universal entire function. Finally we show that Maass forms on the torus are eigenfunctions of the $T\overline T$ deformation. Comment: 19 pages. v2: section on Dirichlet series revised |
| Databáze: | arXiv |
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