Modular invariance and uniqueness of TT¯ deformed CFT

Ofer Aharony, Shouvik Datta, Amit Giveon, Yunfeng Jiang*, David Kutasov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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 TT¯ 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.

Original languageAmerican English
Article number86
JournalJournal of High Energy Physics
Issue number1
StatePublished - 1 Jan 2019

Bibliographical note

Publisher Copyright:
© 2019, The Author(s).


  • Conformal Field Theory
  • Effective Field Theories
  • Field Theories in Lower Dimensions


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