Quiver Chern-Simons theories and 3-algebra orbifolds

TL;DR

This paper explores deriving quiver Chern-Simons theories from Bagger-Lambert theory using orbifold methods, focusing on M2-branes on specific orbifolds and comparing with known models, revealing ambiguities in the process.

Contribution

It introduces a method to obtain quiver Chern-Simons theories from Nambu bracket-based Bagger-Lambert theory via orbifolding, highlighting challenges in matrix regularization.

Findings

Derived quiver theories from Bagger-Lambert framework.

Compared results with ABJM model on orbifolds.

Identified ambiguities in matrix regularization for certain orbifolds.

Abstract

We attempt to derive quiver Chern-Simons-matter theories from the Bagger-Lambert theory with Nambu bracket, through an orbifold prescription which effectively induces a dimensional reduction of the internal space for 3-algebra. We consider M2-branes on an N=4 orbifold $C^2/Z_k\times C^2$, and compare the result with the so-called dual Aharony-Bergman-Jafferis-Maldacena model, proposed recently by Hanany, Vegh, and Zaffaroni. Unlike the N=6 example $C^4/Z_k$, we find ambiguities in the matrix regularization.