Transmission Coefficients from Phantom Currents

TL;DR

This work presents a universal framework for predicting the transmission coefficient across 1+1D conformal interfaces by introducing a spin-2 phantom current that emerges in the folded theory. When a single phantom current is present, the transmission coefficient is fixed solely by the phantom’s conformal dimension, unifying known results (e.g., minimal models, free bosons) and enabling concrete predictions for interfaces yet to be constructed. The approach yields explicit UV–IR maps and $c_{LR}$ expressions in minimal models, reproduces the free-boson result $c_{LR}=\sin^2 2\theta$, and extends to non-unitary examples, while outlining a path to broader generalizations and applications to other observables. Overall, the phantom-current mechanism provides a concise, data-driven criterion for transmission that bypasses full interface details, with potential impact on numerical studies and the algebraic understanding of defect fusion and RG branes.

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.

Figures (1)

• Figure 1: The folding trick enables the reinterpretation of an interface between $\mathrm{CFT}_L$ and $\mathrm{CFT}_R$ as a boundary in $\mathrm{CFT}_L \otimes \overline{\mathrm{CFT}_R}$.