M2 to D2 revisited

By Pei-Ming Ho, Y. Imamura, Yutaka Matsuo. 2008

233 citations recorded by the source corpus.

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 S1 which defines the reduction of M theory to IIA superstring.

Subfields: Algebra and Number Theory, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/583a9aca50e3a3b87f90a5bdc32f4b6437ee65f2

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Citations in the corpus

Generalized conformal symmetry and recovery of SO(8) in multiple M2 and D2 branes (2008, methodology): “An earlier proposal of L-BLG [3, 4, 5] has the desired symmetries, SO(8) and superconformal symmetries but there are several problems.”
M5-brane in three-form flux and multiple M2-branes (2008, methodology): “In [8], the connection with M5 brane was used to provide the geometrical origin of extra generators in the construction of Lie 3-algebra which contains arbitrary Lie algebra.”
Ghost-free superconformal action for multiple M2-branes (2008, background): “Reference [13] observed that if one chooses X + to be constant and Ψ+ to be zero, then the theory reduces to N=8 SYM.”
n-ary algebras: a review with applications (2010, background): “There are models with Lorentzian signature on the 3-Lie algebra [32,275,276], although these immediately raise the question of the unitarity of the quantized theory (see also [277] for this point and [278] for n-Lie algebras with Lorentzian metric).”
Spin Chains in N = 6 Superconformal Chern-Simons-Matter Theory (2008, methodology): “See also [9, 16, 17, 18, 19, 20] for subsequent works on this theory, and [2, 3, 4, 5, 6, 7, 8] for recent works on M2-brane world volume theories.”
A Massive Study of M2-brane Proposals (2008, methodology): “In section 4, we find that this theory based on the Lorentzian three-algebra in [6][7][8] has a unique classical vacuum state.”
Bagger-Lambert Theory for General Lie Algebras (2008, background): “Note added: After this paper appeared, two other papers with closely related results [30, 31 ] appeared in the arXiv.”