Topological Twisting of Multiple M2-brane Theory

TL;DR

This paper performs a topological twist of the Bagger-Lambert-Gustavsson theory, revealing new topological invariants and structures related to multiple M2-branes and M5-branes, with implications for understanding their geometric and quantum properties.

Contribution

It introduces a topological twisting of the Bagger-Lambert-Gustavsson theory with off-shell formalism, connecting M2-brane dynamics to topological invariants like Ray-Singer torsion.

Findings

Constructed a topologically invariant action on curved three-manifolds.

Derived the one-loop partition function as Ray-Singer torsion.

Identified BPS equations involving M2-brane charge density.

Abstract

Bagger-Lambert-Gustavsson theory with infinite dimensional gauge group has been suggested to describe M5-brane as a condensation of multiple M2-branes. Here we perform a topological twisting of the Bagger-Lambert-Gustavsson theory. The original SO(8) R-symmetry is broken to SO(3)XSO(5), where the former may be interpreted as a diagonal subgroup of the Euclidean M5-brane world-volume symmetry SO(6), while the latter is the isometry of the transverse five directions. Accordingly the resulting action contains an one-form and five scalars as for the bosonic dynamical fields. We further lift the action to a generic curved three manifold. In order to make sure the genuine topological invariance, we construct an off-shell formalism such that the scalar supersymmetry transformations are nilpotent strictly off-shell and independent of the metric of the three manifold. The one loop partition function around a trivial background yields the Ray-Singer torsion. The BPS equation involves an M2-brane charge density given by a Nambu-Goto action defined in an internal three-manifold.