# A Defect Verlinde Formula

**Authors:** Ce Shen, Ling-Yan Hung  
**arXiv:** [1901.08285](https://arxiv.org/abs/1901.08285)  
**Date:** 2019-01-24  
**Summary page:** https://www.summarizepaper.com/fr/paper/1901.08285v1/

## Abstract

We revisit the problem of boundary excitations at a topological boundary or junction defects between topological boundaries in non-chiral bosonic topological orders in 2+1 dimensions. Based on physical considerations, we derive a formula that relates the fusion rules of the boundary excitations, and the "half-linking" number between condensed anyons and confined boundary excitations. This formula is a direct analogue of the Verlinde formula. We also demonstrate how these half-linking numbers can be computed in explicit Abelian and non-Abelian examples. As a fundamental property of topological orders and their allowed boundaries, this should also find applications in finding suitable platforms realizing quantum computing devices.