Transmission Coefficients from Phantom Currents

TL;DR

This paper introduces a novel approach using phantom currents to determine transmission coefficients in conformal interfaces, simplifying their calculation and unifying previous results across different models.

Contribution

The work presents a new framework based on phantom currents that completely determines transmission coefficients, providing a unified explanation and new predictions for conformal interface dynamics.

Findings

Transmission coefficient determined by a single phantom current's conformal dimension.

Unified explanation of known results in minimal models and free boson.

Concrete predictions for previously unexplored interfaces.

Abstract

A representative quantity that characterizes the dynamics of conformal interfaces is the transmission coefficient, which is defined through correlation functions of the stress tensor. Typically, this coefficient is complicated and highly dependent on its details. In this work, we introduce a new perspective based on the notion of a ``phantom current''. We have shown that a spin-2 phantom current arising from the folding trick completely determines the transmission coefficient. In particular, when there is a single phantom current, the transmission coefficient is uniquely fixed by its conformal dimension. As a result, our framework provides a unified explanation of known results in minimal models and the free boson, while also yielding concrete predictions for previously unexplored interfaces.