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Modular covariance and uniqueness of \( J\overline{T} \) deformed CFTs

  • Ofer Aharony
  • Shouvik Datta
  • Amit Giveon
  • Yunfeng Jiang
  • David Kutasov
Open Access
Regular Article - Theoretical Physics
  • 12 Downloads

Abstract

We study families of two dimensional quantum field theories, labeled by a dimensionful parameter μ, that contain a holomorphic conserved U(1) current J(z). We assume that these theories can be consistently defined on a torus, so their partition sum, with a chemical potential for the charge that couples to J, is modular covariant. We further require that in these theories, the energy of a state at finite μ is a function only of μ, and of the energy, momentum and charge of the corresponding state at μ = 0, where the theory becomes conformal. We show that under these conditions, the torus partition sum of the theory at μ = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in μ, to be that of a \( \mu J\overline{T} \) deformed conformal field theory (CFT). We derive a flow equation for the \( J\overline{T} \) deformed partition sum, and use it to study non-perturbative effects. We find non-perturbative ambiguities for any non-zero value of μ, 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
  • David Kutasov
    • 4
  1. 1.Department of Particle Physics and AstrophysicsWeizmann Institute of Science, Tel AvivRehovotIsrael
  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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