An Effective Rigid String at \(\theta=\pi\) for the 3D Gauge Theories/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.