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

Understand

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 $g_{\sigma}$.