Spontaneous symmetry breaking in 2D supersphere sigma models and applications to intersecting loop soups

TL;DR

This paper investigates the effects of small coupling on 2D supersphere sigma models, revealing logarithmic corrections and their implications for intersecting loop soups, through perturbative and integrable lattice methods.

Contribution

It provides a detailed analysis of logarithmic corrections in supersphere sigma models using both perturbative field theory and integrable lattice approaches.

Findings

Logarithmic corrections to free theory at small coupling are characterized.

Bethe ansatz confirms perturbative results.

Applications to dense loop soups with crossings are discussed.

Abstract

Two-dimensional sigma models on superspheres $S^{r-1|2s} \cong OSp(r|2s)/OSp(r - 1|2s)$ are known to flow to weak coupling $g_{\sigma} \to 0$ in the IR when $r - 2s < 2$. Their long-distance properties are described by a free 'Goldstone' conformal field theory (CFT) with $r - 1$ bosonic and $2s$ fermionic degrees of freedom, where the $OSp(r|2s)$ symmetry is spontaneously broken. This behavior is made possible by the lack of unitarity. The purpose of this paper is to study logarithmic corrections to the free theory at small but non-zero coupling $g_{\sigma}$. We do this in two ways. On the one hand, we perform perturbative calculations with the sigma model action, which are of special technical interest since the perturbed theory is logarithmic. On the other hand, we study an integrable lattice discretization of the sigma models provided by vertex models and spin chains with $OSp(r|2s)$ symmetry. Detailed analysis of the Bethe equations then confirms and completes the field theoretic calculations. Finally, we apply our results to physical properties of dense loop soups with crossings.