Paperclip at $\theta=\pi$

TL;DR

This paper investigates the paperclip boundary interaction model at a topological angle of π, providing an exact partition function expression and identifying its infrared fixed point through asymptotic analysis.

Contribution

It introduces an exact expression for the disk partition function of the paperclip model at θ=π, linking it to solutions of a differential equation and clarifying its infrared behavior.

Findings

Derived an exact partition function in terms of differential equation solutions.

Identified the infrared fixed point of the boundary flow at θ=π.

Provided asymptotic analysis connecting the partition function to fixed point behavior.

Abstract

We study the ``paperclip'' model of boundary interaction with the topological angle $\theta$ equal to $\pi$. We propose exact expression for the disk partition function in terms of solutions of certain ordinary differential equation. Large distance asymptotic form of the partition function which follows from this proposal makes it possible to identify the infrared fixed point of the paperclip boundary flow at $\theta=\pi$.