Energy Reflection and Transmission of Interfaces in $T\bar{T}$-deformed CFT

TL;DR

The work extends the universal energy-transport framework of interface CFTs to interfaces gluing $T\overline{T}$-deformed CFTs, showing that the deformation can be consistently extended to the interface provided $c_L\mu_L=c_R\mu_R$. It introduces a nonlinear, antisymmetric transmission function that generalizes the linear matching of the undeformed ICFT and computes it explicitly for NESS and scattering states via flow equations. The authors corroborate these field-theory results with holographic calculations in the bulk using mixed boundary conditions and thin-brane models, demonstrating consistent energy transport across deformed interfaces. The results reveal a richer structure of energy transmission, including higher-order nonlinear contributions and frequency-dependent effects, while preserving core conservation laws. These insights offer a controlled setting to probe non-conformal transport in holography and open questions about universality beyond conformal symmetry and UV completeness in $T\overline{T}$-deformed interfaces.

Abstract

Conformal interfaces gluing a pair of two-dimensional conformal field theories enjoy a large degree of universality in terms of the coefficients of reflection and transmission of energy, that describe the scattering of conformal matter at the interface. In this article, we study these coefficients beyond conformality, by gluing a pair of $T\bar T$-deformed 2D CFTs across an interface, which requires the condition $c_L μ_L = c_R μ_R $ to be obeyed. We show that, at least when the interface admits a holographic description, the $T\bar T$ deformation of the CFTs can be extended to the interface. We propose a generalization of the linear matching condition in the universal sector of the undeformed ICFT to a non-linear one, which is captured by a universal antisymmetric \emph{transmission function} of the incoming fluxes. We employ the flow equations of the $T\bar T$-deformed CFTs to compute this function in two special classes of states, namely the non-equilibrium steady state (NESS) and scattering state. We show that the results can also be reproduced using holographic techniques in the bulk dual of these states.

Figures (2)

• Figure 1: Conformal diagram of flat space with a timelike defect separating it into two halves. The figure demonstrates the incident, reflected and transmitted excitation due to the action of a local operator in CFT$_L$. The fluxes are collected at various null infinities.
• Figure 2: The formation of NESS within the lightcone upon gluing two semi-infinite systems at temperatures $\theta_L$ and $\theta_R$. The NESS forms within the lightcone (III). In the presence of the defect, the NESS region further subdivides into IIIA and IIIB.