$T\overline{T}$-deformed modular forms

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.

19 pages. v2: section on Dirichlet series revised

References in corpus (2)

• On space of integrable quantum field theories
• Harmonic analysis of 2d CFT partition functions

Cited by in corpus (9)

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• Systematic approach to correlators in $T\bar{T}$ deformed CFTs
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Massive Theta Lifts
• $T\bar{T}$ deformed scattering happens within matrices
• Manifest Modular Invariance in the Near-Critical Ising Model