The Bagger-Lambert model and Type IIA string theory

TL;DR

This paper proposes a conjecture for a compactified Fukaya's homology with a 2-Gerstenhaber algebra structure, aiming to shed light on the 2-Lie algebra in D-brane models.

Contribution

It introduces a conjecture for a new form of Fukaya's homology with a 2-Gerstenhaber algebra structure, connecting symplectic geometry and string theory.

Findings

Conjecture of a compactified Fukaya's homology with 2-Gerstenhaber structure

Potential implications for understanding 2-Lie algebra in D-brane models

Bridging symplectic geometry with string theory concepts

Abstract

We conjecture the existence of a `compactified' version of Fukaya's homology for symplectic manifolds, which carries a canonical 2-Gerstenhaber algebra structure. This may help to understand the 2-Lie algebra structure involved in models for interacting D-branes.