Accidental Symmetries and the Conformal Bootstrap

TL;DR

This paper investigates an ${ m N}=2$ supersymmetric 3D $O(N)$ model, showing symmetry enhancement at the IR fixed point via bootstrap and localization, and constraining possible models with bootstrap bounds and the $F$-theorem.

Contribution

It combines conformal bootstrap and supersymmetric localization to analyze symmetry enhancement and constraints in a supersymmetric $O(N)$ model, extending results to fractional dimensions.

Findings

Symmetry enhancement occurs at the IR fixed point when $g_2$ flows to zero.

Bootstrap bounds exclude models with $g_1,g_2 eq 0$ for $N>2$.

Models with $g_2=0$ approach bootstrap bounds, indicating near-saturation.

Abstract

We study an ${\cal N} = 2$ supersymmetric generalization of the three-dimensional critical $O(N)$ vector model that is described by $N+1$ chiral superfields with superpotential $W = g_1 X \sum_i Z_i^2 + g_2 X^3$. By combining the tools of the conformal bootstrap with results obtained through supersymmetric localization, we argue that this model exhibits a symmetry enhancement at the infrared superconformal fixed point due to $g_2$ flowing to zero. This example is special in that the existence of an infrared fixed point with $g_1,g_2\neq 0$, which does not exhibit symmetry enhancement, does not generally lead to any obvious unitarity violations or other inconsistencies. We do show, however, that the $F$-theorem excludes the models with $g_1,g_2\neq 0$ for $N>5$. The conformal bootstrap provides a stronger constraint and excludes such models for $N>2$. We provide evidence that the $g_2=0$ models, which have the enhanced $O(N)\times U(1)$ symmetry, come close to saturating the bootstrap bounds. We extend our analysis to fractional dimensions where we can motivate the nonexistence of the $g_1,g_2\neq 0$ models by studying them perturbatively in the $4-\epsilon$ expansion.