Symmetries versus the spectrum of $J\bar{T}$-deformed CFTs

Abstract

It has been recently shown that classical $J\bar{T}$ - deformed CFTs possess an infinite-dimensional Witt-Kač-Moody symmetry, generated by certain field-dependent coordinate and gauge transformations. On a cylinder, however, the equal spacing of the descendants' energies predicted by such a symmetry algebra is inconsistent with the known finite-size spectrum of $J\bar{T}$ - deformed CFTs. Also, the associated quantum symmetry generators do not have a proper action on the Hilbert space. In this article, we resolve this tension by finding a new set of (classical) conserved charges, whose action is consistent with semi-classical quantization, and which are related to the previous symmetry generators by a type of energy-dependent spectral flow. The previous inconsistency between the algebra and the spectrum is resolved because the energy operator does not belong to the spectrally flowed sector.

arXiv commentfixed a minus sign; various minor cosmetic changes; added a brief discussion

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Cited by in corpus (6)

• 3D Gravity in a Box
• Infinite pseudo-conformal symmetries of classical $T\bar{T}$, $J\bar{T}$ and $J{T}_a$ - deformed CFTs
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• A definition of primary operators in $J\bar{T}$-deformed CFTs
• States, symmetries and correlators of $T\bar{T}$ and $J\bar{T}$ symmetric orbifolds
• Characters of irrelevant deformations