Abstract
Any two dimensional quantum field theory that can be consistently defined on a torus is invariant under modular transformations. In this paper we study families of quantum field theories labeled by a dimensionful parameter t, that have the additional property that the energy of a state at finite t is a function only of t and of the energy and momentum of the corresponding state at t = 0, where the theory becomes conformal. We show that under this requirement, the partition sum of the theory at t = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in t, to be that of a \( T\overline{T} \) deformed CFT. Non-perturbatively, we find that for one sign of t (for which the energies are real) the partition sum is uniquely determined, while for the other sign we find non-perturbative ambiguities. We characterize these ambiguities and comment on their possible relations to holography.
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Aharony, O., Datta, S., Giveon, A. et al. Modular invariance and uniqueness of \( T\overline{T} \) deformed CFT. J. High Energ. Phys. 2019, 86 (2019). https://doi.org/10.1007/JHEP01(2019)086
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DOI: https://doi.org/10.1007/JHEP01(2019)086