Entropy of conformal perturbation defects

TL;DR

This paper develops a perturbative framework for conformal perturbation defects arising from short bulk RG flows between 2D CFTs. It derives a universal formula for the defect boundary entropy, $g_\phi^2 = 1 + \delta^2/(2C^2) + \delta^3 D/C^4 + \mathcal O(\delta^4)$, where $C$ is the leading OPE coefficient and $D$ is a universal cubic coefficient, using a Wilsonian renormalization scheme. The leading correction is fixed by the OPE data, and the cubic term is scheme-independent up to $\mathcal O(\delta)$, providing a robust probe of bulk-defect correspondence. Applying the result to flows between neighboring minimal models with $\phi_{1,3}$ perturbations, the authors find exact agreement with Gaiotto's RG-domain-wall defect to the first two orders, reinforcing the interpretation of Gaiotto's defect as a perturbation defect for these flows.

Abstract

We consider perturbation defects obtained by perturbing a 2D conformal field theory (CFT) by a relevant operator on a half-plane. If the perturbed bulk theory flows to an infrared fixed point described by another CFT, the defect flows to a conformal defect between the ultraviolet and infrared fixed point CFTs. For short bulk renormalization group flows connecting two fixed points which are close in theory space we find a universal perturbative formula for the boundary entropy of the corresponding conformal perturbation defect. We compare the value of the boundary entropy that our formula gives for the flows between nearby Virasoro minimal models Mm with the boundary entropy of the defect constructed by Gaiotto in [1] and find a match at the first two orders in the 1/m expansion.