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arXiv · 2201.00478

$T\overline T$-deformed modular forms

John Cardy
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Abstract

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.

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John Cardy. 2022-01-03. $T\overline T$-deformed modular forms. https://doi.org/10.4310/cntp.2022.v16.n3.a1

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