Bagger-Lambert theory on an orbifold and its relation to Chern-Simons-matter theories

Details Bagger-Lambert theory on an orbifold and its relation to Chern-Simons-matter theories Bagger-Lambert theory on an orbifold and its relation to Chern-Simons-matter theories

2008-07-09

arxiv.org/abs/0807.1349v3

Phys.Rev.D81:086006,2010

Physics

High Energy Physics

High Energy Physics - Theory

20 pages; v3. major revision, title and abstract changed. to appear in Phys.Rev.D

Scientific paper

10.1103/PhysRevD.81.086006

We consider how to take an orbifold reduction for the multiple M2-brane theory recently proposed by Bagger and Lambert, and discuss its relation to Chern-Simons theories. Starting from the infinite dimensional 3-algebra realized as the Nambu bracket on a 3-torus, we first suggest an orbifolding prescription for various fields. Then we introduce a second truncation, which effectively reduces the internal space to a 2-torus. Eventually one obtains a large-N limit of Chern-Simons gauge theories coupled to matter fields. We consider an abelian orbifold C^4/Z_n, and illustrate how one can arrive at the N=6 supersymmetric theories with gauge groups U(N) x U(N) and Chern-Simons levels (k,-k), as recently constructed by Aharony, Bergman, Jafferis and Maldacena.

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