ZN symmetries, anomalies, and the modular bootstrap

We explore constraints on (1 + 1)d unitary conformal field theory with an internal Z(N) global symmetry, by bounding the lightest symmetry-preserving scalar primary operator using the modular bootstrap. Among the other constraints we have found, we prove the existence of a Z(N)-symmetric relevant/marginal operator if N - 1 <= c <= 9 - N for N <= 4, with the end points saturated by various Wess-Zumino-Witten models that can be embedded into (e(8))(1). Its existence implies that robust gapless fixed points are not possible in this range of c if only a Z(N) symmetry is imposed microscopically. We also obtain stronger, more refined bounds that depend on the 't Hooft anomaly of the Z(N) symmetry.

Automated summary

This paper explores constraints on (1 + 1)d unitary conformal field theory with an internal Z(N) global symmetry, by bounding the lightest symmetry-preserving scalar primary operator using the modular bootstrap. Amongst other constraints found, it is proven that a Z(N)-symmetric relevant/marginal operator exists under specific conditions, with stronger bounds dependent on the 't Hooft anomaly of the Z(N) symmetry.