Non-Abelian Tensor Towers and (2,0) Superconformal Theories

TL;DR

This paper constructs a five-dimensional superconformal action with an infinite tower of non-Abelian tensors and vectors to model six-dimensional (2,0) superconformal theories compactified on a circle, exploring supersymmetry enhancement and anomaly cancellation.

Contribution

It introduces a novel superconformal action incorporating an infinite tower of non-Abelian tensor multiplets, extending the understanding of (2,0) theories and supersymmetry restoration techniques.

Findings

Recovered maximally supersymmetric Yang-Mills theories as special cases.

Constructed a coupling of super-Yang-Mills to an infinite tower of massive non-Abelian tensors.

Commented on anomaly cancellation via a Wess-Zumino term at one loop.

Abstract

With the aim to study six-dimensional (2,0) superconformal theories with non-Abelian tensor multiplets we propose a five-dimensional superconformal action with eight supersymmetries for an infinite tower of non-Abelian vector, tensor and hypermultiplets. It describes the dynamics of the complete spectrum of the (2,0) theories compactified on a circle coupled to an additional vector multiplet containing the circle radius and the Kaluza-Klein vector arising from the six-dimensional metric. All couplings are only given in terms of group theoretical constants and the Kaluza-Klein levels. After superconformal symmetry is reduced to Poincare supersymmetry we find a Kaluza-Klein inspired action coupling super-Yang-Mills theory to an infinite tower of massive non-Abelian tensors. We explore the possibility to restore sixteen supersymmetries by using techniques known from harmonic superspace. Namely, additional bosonic coordinates on a four-sphere are introduced to enhance the R-symmetry group. Maximally supersymmetric Yang-Mills theories and the Abelian (2,0) tensor theories are recovered as special cases of our construction. Finally, we comment on the generation of an anomaly balancing Wess-Zumino term for the R-symmetry vector at one loop.