paper

The holographic interpretation of -deformed CFTs

arXiv:1803.09753 · doi:10.1007/JHEP01(2019)198

Abstract

Recently, a non-local yet possibly UV-complete quantum field theory has been constructed by deforming a two-dimensional CFT by the composite operator , where is a chiral current and is a component of the stress tensor. Assuming the original CFT was a holographic CFT, we work out the holographic dual of its deformation. We find that the dual spacetime is still AdS, but with modified boundary conditions that mix the metric and the Chern-Simons gauge field dual to the current. We show that when the coefficient of the chiral anomaly for 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 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.

arXiv commentv2: added discussion of the chiral anomaly and one appendix, affiliation and grant information updated

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