On Superspace Chern-Simons-like Terms

TL;DR

This paper investigates superspace Chern-Simons-like terms in four-dimensional N=2 supersymmetric theories, identifying a class of globally nontrivial four-derivative terms classified by Dolbeault cohomology, revealing new global obstructions.

Contribution

It introduces a classification of superspace Chern-Simons-like terms using Dolbeault cohomology and discusses their global obstructions in the effective action.

Findings

Identifies a class of four-derivative terms with global obstructions.

Classifies these terms via Dolbeault cohomology on the moduli space.

Highlights the difference between local and global descriptions of these terms.

Abstract

We search for superspace Chern-Simons-like higher-derivative terms in the low energy effective actions of supersymmetric theories in four dimensions. Superspace Chern-Simons-like terms are those gauge-invariant terms which cannot be written solely in terms of field strength superfields and covariant derivatives, but in which a gauge potential superfield appears explicitly. We find one class of such four-derivative terms with N=2 supersymmetry which, though locally on the Coulomb branch can be written solely in terms of field strengths, globally cannot be. These terms are classified by certain Dolbeault cohomology classes on the moduli space. We include a discussion of other examples of terms in the effective action involving global obstructions on the Coulomb branch.