The holographic interpretation of $J \bar T$-deformed CFTs
Résumé
Recently, a non-local yet possibly UV-complete quantum field theory has been constructed by deforming a two-dimensional CFT by the composite operator $ J\overline{T} $ , where J is a chiral U(1) current and $ \overline{T} $ is a component of the stress tensor. Assuming the original CFT was a holographic CFT, we work out the holographic dual of its $ J\overline{T} $ deformation. We find that the dual spacetime is still AdS$_{3}$, but with modified boundary conditions that mix the metric and the Chern-Simons gauge field dual to the U(1) current. We show that when the coefficient of the chiral anomaly for J vanishes, the energy and thermodynamics of black holes obeying these modified boundary conditions precisely reproduce the previously derived field theory spectrum and thermodynamics. Our proposed holographic dictionary can also reproduce the field-theoretical spectrum in presence of the chiral anomaly, upon a certain assumption that we justify. The asymptotic symmetry group associated to these boundary conditions consists of two copies of the Virasoro and one copy of the U(1) Kač-Moody algebra, just as before the deformation, the only effect of the latter is to modify the spacetime dependence of the right-moving Virasoro generators, whose action becomes state-dependent and effectively non-local.
Mots clés
AdS-CFT Correspondence
Conformal Field Theory
Chern-Simons Theories
field theory: conformal
duality: holography
gauge field theory: duality
space-time: duality
black hole: thermodynamics
operator: composite
tensor: energy-momentum
dimension: 2
U(1)
boundary condition
deformation
nonlocal
Virasoro
space-time dependence
field theory
Chern-Simons term
anti-de Sitter
algebra
chiral