Reduction of the N=8 BLG and N=6 BL Theories to 2D Effective Field Theories

TL;DR

This paper reduces 3D N=8 BLG and N=6 BL theories to 2D effective field theories, aiming to describe F1 strings in type IIA, revealing how their actions transform under dimensional reduction.

Contribution

It provides a novel reduction of BLG and BL theories to 2D, connecting M2-brane theories to F1 string actions in type IIA superstring theory.

Findings

Reduction of CS term to Phi*F term

Scalars and fermions acquire mass terms

Reduced actions still rely on three-algebra structure

Abstract

Starting from the three dimensional N=8 BLG and N=6 BL theories with CS level k=1, a dimensional reduction is performed on the M2-branes worldvolume. The IR limit of these 2D EFTs should represent the action of F1 strings in type IIA. The CS term reduces to a particular Phi*F term and the scalars and fermions get "mass" terms. The reduced actions still rely on three-algebra, which we did not require to define precisely.