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Modular invariance and uniqueness of \( T\overline{T} \) deformed CFT

  • Ofer Aharony
  • Shouvik Datta
  • Amit Giveon
  • Yunfeng JiangEmail author
  • David Kutasov
Open Access
Regular Article - Theoretical Physics
  • 11 Downloads

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.

Keywords

Conformal Field Theory Effective Field Theories Field Theories in Lower Dimensions 

Notes

Open Access

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.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Ofer Aharony
    • 1
  • Shouvik Datta
    • 2
  • Amit Giveon
    • 3
  • Yunfeng Jiang
    • 2
    Email author
  • David Kutasov
    • 4
  1. 1.Department of Particle Physics and AstrophysicsWeizmann Institute of ScienceRehovotIsrael
  2. 2.Institut für Theoretische PhysikETH ZürichZürichSwitzerland
  3. 3.Racah Institute of PhysicsThe Hebrew UniversityJerusalemIsrael
  4. 4.EFI and Department of PhysicsUniversity of ChicagoChicagoU.S.A.

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