Entanglement renormalization of a $$ \mathrm{T}\overline{\mathrm{T}} $$-deformed CFT

Abstract

Abstract In this work we use cMERA, a continuous tensor network, to find a Gaussian approximation to the ground state of a T$$ \overline{T} $$ T ¯ -deformed scalar CFT on the line, to first order in the deformation parameter. The result is used to find the correction to the correlators of scaling operators of the theory and to the entanglement entropy of a half-line. From the latter, we discuss the non-localities induced by the T$$ \overline{T} $$ T ¯ deformation at short length scales. We find that the kind of non-locality generated by those terms can be considered as a mild-one, in the sense that it does not violate the area law of entanglement. In the context of the conjectured connection between cMERA and holography, we find that at first insight a finite bulk radius can be defined in the putative geometric dual description of cMERA. However, the entropy analysis contradicts the proposal that no geometry can be ascribed to the region outside this radial cutoff.