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Résumé |
I will start with a brief review of the irrelevant current-current
deformations of two-dimensional QFTs introduced by Smirnov and
Zamolodchikov, concentrating on the $T\bar T, J\bar T $ and $ JT_a$ ones. I
will then show that classical $T\bar T, J\bar T $ and $ JT_a$ -deformed CFTs
possess an infinite set of symmetries that take the form of a field-
dependent generalization of two-dimensional conformal and, if applicable,
$U(1)$ transformations. The Poisson bracket algebra of the associated
conserved charges consists of two commuting copies of a functional Witt -
(Ka\v{c}-Moody) algebra. One notes, however, that at semi-classical level on
a cylinder, the equal spacing of the descendants' energies predicted by such
a symmetry algebra is inconsistent with the known finite-size spectrum of
the deformed CFTs. I will show how to resolve this tension in the specific
case of $J\bar T$ - deformed CFTs, by exhibiting a new set of (classical)
conserved charges, which are related to the previous symmetry generators by
a type of energy-dependent spectral flow. The above results suggest then
that $T\bar T, J\bar T $ and $ JT_a$ -deformed CFTs correspond to non-local
versions of usual two-dimensional conformal field theories, a structure that
would be interesting to explore further. \\ \\ The seminar is online only.
\\ Internet link to be collected from the Organizer: Vincent Pasquier
(vincent.pasquier@ipht.fr) |
