On Non-linear Action for Gauged M2-brane

TL;DR

This paper develops a non-linear extension of the abelian ABJM model with higher derivative corrections, demonstrating its consistency with M2-brane physics, including the Higgs mechanism and BPS solutions, and discusses potential generalizations.

Contribution

It introduces a non-linear, higher-derivative corrected abelian ABJM model that accurately describes a single M2-brane with background couplings and confirms the Higgs mechanism's validity.

Findings

The model reproduces the Dirac-Born-Infeld action with Wess-Zumino term.

Half BPS solutions are found, representing intersecting M2-branes.

The Higgs mechanism remains valid with higher derivative corrections.

Abstract

We propose a non-linear extension of U(1) \times U(1) (abelian) ABJM model including T_{M2} (higher derivative) corrections. The action proposed here is expected to describe a single M2-brane proving C^4/Z_k target space. The model includes couplings with the 3-form background in the eleven-dimensional supergravity which is consistent with the orbifold projection. We show that the novel higgs mechanism proposed by Mukhi and Papageorgakis does work even in the presence of higher derivative corrections and couplings with the background field, giving the correct structure of the Dirac-Born-Infeld action with Wess-Zumino term for a D2-brane. We also find half BPS solutions in the full non-linear theory which is interpreted as an another M2-brane intersecting with the original M2-brane. A possible generalization to U(N) \times U(N) gauge group is briefly discussed.