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

TL;DR

The paper proposes a five-dimensional \\mathcal{N}=2 superconformal action that captures the full Kaluza-Klein tower of non-Abelian tensor, vector, and hypermultiplets arising from circle-compactified six-dimensional \\,(2,0) theories. The construction relies on KK gauging, a careful split to \\mathcal{N}=2 multiplets, and a harmonic-superspace inspired enhancement to \\mathcal{N}=4 via USp(4)_R covariantization, yielding CS-like kinetic terms for tensors and a consistent non-Abelian gauging framework. In special limits, the zero-mode sector reduces to Maximally SUSY Yang-Mills (\\mathcal{N}=4) and the Abelian (2,0) tensor theory, while a detailed one-loop analysis of anomaly terms demonstrates that KK modes do not spoil the expected large-N scaling of the Wess-Zumino term, supporting a six-dimensional origin. The work offers a promising lower-dimensional action framework to investigate the elusive \\(2,0) theories, their conformal anomalies, and their M5-brane dynamics, while outlining clear avenues for restoring full six-dimensional symmetries and clarifying quantum properties.

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.

Figures (1)

• Figure 1: One-loop four-point diagram with external background fields.