An Effective Rigid String at $\theta=\pi$ for the 3D Gauge Theories/Ising Model

TL;DR

This paper proposes an effective sigma model for the 3D rigid string with a theta-term at pi, revealing a fixed point with long-range correlations and potential applications to 3D gauge theories and the Ising model.

Contribution

It introduces a novel effective theory combining the SU(2) WZW model with the Nambu-Goto action for the 3D rigid string at theta=pi, including non-perturbative corrections.

Findings

Existence of an IR fixed point with long-range correlations

Effective theory includes non-perturbative genus corrections

Potential description of critical behavior in 3D gauge theories and Ising model

Abstract

An effective sigma model describing behavior of the 3d rigid string with a $\theta$-term at $\theta=\pi$ is proposed. It contains non-perturbative corrections resulting from summation over different genera of the 2d surfaces. The effective theory is the SU(2) WZW model coupled to the Nambu-Goto action. RG analysis shows the existence of a IR fixed point at which the normal to the surface has long range correlations. A similar model can describe critical behaviour of the 3d Y-M fields or the Ising model.