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arXiv · 0805.1202

M2 to D2 revisited

Pei-Ming Ho·Yosuke Imamura·Yutaka Matsuo
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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.

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Pei-Ming Ho, Yosuke Imamura, Yutaka Matsuo. 2008-05-21. M2 to D2 revisited. https://doi.org/10.1088/1126-6708%2F2008%2F07%2F003

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