# Defects in the Tri-critical Ising model

## TL;DR

This paper constructs new conformal defects in the tri-critical Ising model by leveraging fermionic theories and interface defects, expanding understanding of defect structures in conformal field theories.

## Contribution

It introduces a novel method to construct conformal defects in the minimal model using fermionic theories and interface defects, including topological defect analysis.

## Key findings

- Constructed new conformal defects in the minimal model.
- Identified topological defects and interfaces in fermionic theories.
- Analyzed defects in free fermion and Ising model as foundational steps.

## Abstract

We consider two different conformal field theories with central charge c=7/10. One is the diagonal invariant minimal model in which all fields have integer spins; the other is the local fermionic theory with superconformal symmetry in which fields can have half-integer spin. We construct new conformal (but not topological or factorised) defects in the minimal model. We do this by first constructing defects in the fermionic model as boundary conditions in a fermionic theory of central charge c=7/5, using the folding trick as first proposed by Gang and Yamaguchi. We then acting on these with interface defects to find the new conformal defects. As part of the construction, we find the topological defects in the fermionic theory and the interfaces between the fermionic theory and the minimal model. We also consider the simpler case of defects in the theory of a single free fermion and interface defects between the Ising model and a single fermion as a prelude to calculations in the tri-critical Ising model.