(1,0) superconformal models in six dimensions

TL;DR

The paper constructs a broad class of six-dimensional (1,0) superconformal models with non-abelian couplings between multiple tensor multiplets and Yang–Mills fields by employing an extended tensor hierarchy that includes three-form gauge potentials. Supersymmetry closes on-shell, yielding first-order duality relations that bind the vector and tensor sectors without adding propagating degrees of freedom; a Lagrangian formulation exists only for a subclass, but generically implies an indefinite kinetic metric and potential ghosts. The authors analyze vacuum structures and linearized excitations, showing how scalar vevs control inverse Yang–Mills couplings and how protected multiplet content arises in perturbation theory, including novel non-decomposable TV/VT couplings. They provide explicit models, notably an SO(5) gauge theory with a corresponding action and a nilpotent N8-based model, and discuss extensions to hypermultiplets toward (2,0) content, as well as questions on quantization, anomalies, and the relation to M-brane dynamics.

Abstract

We construct six-dimensional (1,0) superconformal models with non-abelian gauge couplings for multiple tensor multiplets. A crucial ingredient in the construction is the introduction of three-form gauge potentials which communicate degrees of freedom between the tensor multiplets and the Yang-Mills multiplet, but do not introduce additional degrees of freedom. Generically these models provide only equations of motions. For a subclass also a Lagrangian formulation exists, however it appears to exhibit indefinite metrics in the kinetic sector. We discuss several examples and analyze the excitation spectra in their supersymmetric vacua. In general, the models are perturbatively defined only in the spontaneously broken phase with the vev of the tensor multiplet scalars serving as the inverse coupling constants of the Yang-Mills multiplet. We briefly discuss the inclusion of hypermultiplets which complete the field content to that of superconformal (2,0) theories.