M2 to D2 revisited

Abstract

We present two derivations of the multiple D2 action from the multiple M2-brane model proposed by Bagger-Lambert and Gustavsson. The first one is to start from Lie 3-algebra associated with given (arbitrary) Lie algebra. The Lie 3-algebra metric is not positive definite but the zero-norm generators merely correspond to Lagrange multipliers. Following the work of Mukhi and Papageorgakis, we derive D2-brane action from the model by giving a variable a vacuum expectation value. The second derivation is based on the correspondence between M2 and M5. We compactify one dimension and wind M5 brane along this direction. This leads to a noncommutative D4 action. Multiple D2 action is then obtained by suitably choosing the non-commutative parameter on the two-torus. It also implies a natural interpretation to the extra generator in Lie 3-algebra, namely the winding of M5 world volume around $S^1$ which defines the reduction of M theory to \IIA superstring.

20 pages, minor modifications, references added

References in corpus (13)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Comments on Multiple M2-branes
• Comments on the Bagger-Lambert theory and multiple M2-branes
• Membranes on an Orbifold
• Constraining Maximally Supersymmetric Membrane Actions
• N = 8 Superconformal Chern--Simons Theories
• Mass-Deformed Bagger-Lambert Theory and its BPS Objects
• Exploring Pure Spinor String Theory on AdS_4 x CP^3
• Multiple M2-branes and the Embedding Tensor
• Aspects of Multiple Membranes
• On the structure of k-Lie algebras

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