One-loop corrections to Bagger-Lambert theory

TL;DR

This paper reformulates the Bagger-Lambert theory as a Chern-Simons action, computes one-loop quantum corrections, and shows that the coupling constant remains unrenormalized due to the underlying Lie 3-algebra structure.

Contribution

It presents a new formulation of Bagger-Lambert theory using standard Chern-Simons action and demonstrates non-renormalization of the coupling constant.

Findings

Reformulation as Chern-Simons action for any Lie 3-algebra

One-loop self-energy and vertex corrections computed

Coupling constant remains unrenormalized due to Lie 3-algebra structure

Abstract

We rewrite the Bagger-Lambert action for any Lie 3-algebra as a standard Chern- Simons action coupled to matter. We use this action to compute self-energies and vertex corrections at one-loop order. Non-renormalization of the coupling constant comes out as a direct consequence of the Lie 3-algebra structure underlying the Lie algebra.