Tensor and Vector Multiplets in Six-Dimensional Supergravity

TL;DR

Ferrara, Riccioni, and Sagnotti construct the complete coupling of six-dimensional $$(1,0)$$ supergravity to $n$ tensor multiplets and extend it to include vector multiplets via a generalized Green-Schwarz mechanism. They derive the full supersymmetry algebra, supercovariant field strengths, and self-duality constraints, enforcing Wess-Zumino consistency to determine residual anomalies and their fermionic completions; a quartic gaugino coupling introduces a 2-cocycle extension that preserves on-shell closure. The work elucidates how gauge and supersymmetry anomalies are canceled in 6D vacua and highlights the nontrivial algebraic structures these anomalies induce, including a central-like extension in the gaugino sector and associated deformations of the tensor and gravitino transformations. It also discusses potential Lagrangian formulations (e.g., PST-inspired for tensor multiplets), the role of singular gauge couplings, and implications for string dualities and perturbative/type-I vacua in six dimensions.

Abstract

We construct the complete coupling of $(1,0)$ supergravity in six dimensions to $n$ tensor multiplets, extending previous results to all orders in the fermi fields. We then add couplings to vector multiplets, as dictated by the generalized Green-Schwarz mechanism. The resulting theory embodies factorized gauge and supersymmetry anomalies, to be disposed of by fermion loops, and is determined by corresponding Wess-Zumino consistency conditions, aside from a quartic coupling for the gaugini. The supersymmetry algebra contains a corresponding extension that plays a crucial role for the consistency of the construction. We leave aside gravitational and mixed anomalies, that would only contribute to higher-derivative couplings.