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arXiv · 2012.15806

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

Monica Guica
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Abstract

It has been recently shown that classical $J\bar T$ - deformed CFTs possess an infinite-dimensional Witt-Ka\v{c}-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.

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Monica Guica. 2020-12-31. Symmetries versus the spectrum of $ J\bar T$-deformed CFTs. https://doi.org/10.21468/scipostphys.10.3.065

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