# Entanglement entropy at CFT junctions

## TL;DR

This paper studies entanglement entropy at junctions of multiple (1+1)-dimensional free boson and fermion CFTs, revealing universal behaviors and specific divergences depending on the number of theories involved.

## Contribution

It extends entanglement entropy analysis to N-junctions of free CFTs, deriving universal and divergent terms and exploring specific geometries for N=3.

## Key findings

- Universal form of entanglement entropy depends on total transmission and zero mode volume.
- For N>2, a sub-leading divergence appears independent of junction parameters.
- Explicit calculations for N=3 geometries illustrate the theoretical results.

## Abstract

We consider entanglement through permeable junctions of $N$ $(1+1)$-dimensional free boson and free fermion conformal field theories. In the folded picture we constrain the form of the general boundary state. We calculate replicated partition functions with interface operators inserted in the partially-folded picture, from which the entanglement entropy is calculated. The functional form of the universal and constant terms are the same as the $N=2$ case, depending only of the total transmission of the junction and the unit volume of the zero mode lattice. For $N>2$ we see a sub-leading divergent term which does not depend on the parameters of the junction. For $N=3$ we consider some specific geometries and discuss various limits.