The Critical Ising Model on a M\"obius Strip

TL;DR

This paper investigates the critical Ising model on a M"obius strip using conformal field theory, deriving explicit boundary state representations and analyzing the duality in partition functions.

Contribution

It introduces a Majorana fermion field theory approach to explicitly construct crosscap states and explores the duality structure of the partition functions for the model.

Findings

Explicit crosscap state representations derived

Duality relations in partition functions analyzed

Application of Majorana fermion theory to boundary conditions

Abstract

We study the two-dimensional critical Ising model on a M\"obius strip based on a duality relation between conformally invariant boundary conditions. By using a Majorana fermion field theory, we obtain explicit representations of crosscap states corresponding to the boundary states. We also discuss the duality structure of the partition functions.