Holomorphic Surface Defects in Four-Dimensional Chern-Simons Theory

TL;DR

This paper investigates the framing anomaly in four-dimensional holomorphic-topological Chern-Simons theory, revealing its role in coupling to holomorphic theories with Kac-Moody symmetry and enabling the existence of holomorphic monodromy defects.

Contribution

It derives the framing anomaly in 4D holomorphic Chern-Simons theory and shows how it facilitates coupling to Kac-Moody symmetric theories and the construction of monodromy defects.

Findings

Framing anomaly in 4D holomorphic Chern-Simons derived.

Coupling to Kac-Moody symmetric theories at critical level established.

Existence of holomorphic monodromy defects demonstrated.

Abstract

We derive the framing anomaly of four-dimensional holomorphic-topological Chern-Simons theory formulated on the product of a topological surface and the complex plane. We show that the presence of this anomaly allows one to couple four-dimensional Chern-Simons theory to holomorphic field theories with Kac-Moody symmetry, where the Kac-Moody level $k$ is critical $k=-h^{\vee}$. Applying this result to a holomorphic sigma model into a complex coadjoint orbit, we derive that four-dimensional Chern-Simons theory admits holomorphic monodromy defects.