# Five-dimensional Super-Yang-Mills and its Kaluza-Klein tower

## TL;DR

This paper explores the compactification of a 6d abelian tensor multiplet to 5d super-Yang-Mills, including all Kaluza-Klein modes, revealing a nonlocal superconformal symmetry and proposing a nonabelian extension.

## Contribution

It introduces a framework for including all KK modes in 5d SYM with superconformal symmetry, extending previous models to a nonabelian setting.

## Key findings

- Classical abelian 6d tensor multiplet reduces to 5d SYM with KK modes.
- Nonlocal superconformal symmetry is preserved in the abelian case.
- Nonabelian generalization maintains KK modes with nonlocal symmetry, but local symmetry is limited.

## Abstract

We compactify the abelian 6d (1,0) tensor multiplet on a circle bundle, thus reducing the theory down to 5d SYM while keeping all the KK modes. This abelian classical field theory, when interpreted suitably, has a nonlocal superconformal symmetry. Furthermore, a nonabelian generalization, where all the KK modes are kept, is possible for the nonlocal superconformal symmetry, whereas for the local superconformal symmetry we can only realize a subgroup.