Kavli Affiliate: Huajia Wang
| First 5 Authors: Wen-Xin Lai, Wen-Xin Lai, , ,
| Summary:
Turning on the $TbarT$-deformation in a two-dimensional CFT provides a
unique window to study explicitly how non-local features arise in the UV as a
result of the deformation. A sharp signature is the dynamical emergence of an
effective length-scale $propto sqrtmu$ that separates the local and
non-local regimes of the deformed theory, effectively serving as a UV cut-off
for computing observables in the local regime. In this paper, we study this
phenomenon through the entanglement structures of the deformed theory. We focus
on computing the Renyi entropies of single-interval sub-regions in the deformed
vacuum states. We pay particular attention to the interplay between the bare
entanglement cut-off inherited from the CFT computation and the effects from
the $TbarT$ deformations. Applying the general replica trick to the string
theory formulation of $TbarT$-deformed CFTs, we derive an explicit
representation of the deformed replica partition function as a weighted
integral of the CFT results evaluated at a dynamical cut-off, which is
integrated over. We computed in detail the kernel functions of the integral
representation, and performed the saddle-point analysis in the semi-classical
limit of small $mu$. We found that in addition to the perturbative
saddle-point which identifies the dynamical cut-off with the bare entanglement
cut-off, there exists another non-perturbative saddle-point that identifies the
dynamical cut-off with the $TbarT$ length-scale $propto sqrtmu$, but
whose contribution is exponentially small. We discuss how these
non-perturbative effects can shed lights on the mechanism through which the
$TbarT$ length-scale may eventually replace the bare counter-part and become
the effective entanglement cut-off.
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