Five-dimensional SYM from undeformed ABJM

TL;DR

This paper derives a five-dimensional super Yang-Mills theory from undeformed ABJM by expanding around a specific vacuum, revealing a circle-bundle structure and coupling to a background two-form.

Contribution

It provides a novel derivation of 5D SYM from ABJM theory via vacuum expansion, elucidating geometric and coupling properties.

Findings

Derivation of 5D SYM from ABJM via vacuum expansion

Identification of a circle-bundle structure with a singularity

Coupling to a background two-form in the resulting theory

Abstract

We expand undeformed ABJM theory around the vacuum solution that was found in arxiv:0909.3101. This solution can be interpreted as a circle-bundle over a two-dimensional plane with a singularity at the origin. By imposing periodic boundary conditions locally far away from the singularity, we obtain a local fuzzy two-torus over which we have a circle fibration. By performing fluctuation analysis we obtain five-dimensional SYM with the precise value on the coupling constant that we would obtain by compactifying multiple M5 branes on the vacuum three-manifold. In the resulting SYM theory we also find a coupling to a background two-form.