Symmetries versus the spectrum of J(T)over-bar - deformed CFTs

It has been recently shown that classical J (T) over bar - deformed CFTs possess an infinite-dimensional Witt-Kac-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 (T) over bar - 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 semiclassical 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.

Automated summary

A new set of conserved charges has been found in classical J (T) over bar - deformed CFTs, resolving a contradiction and reconciling the inconsistency between symmetry generators and the spectrum.