Bagger-Lambert Theory for General Lie Algebras

By Joaquim Gomis, G. Milanesi, Jorge G. Russo. 2008

217 citations recorded by the source corpus.

We construct the totally antisymmetric structure constants f^{ABCD} of a 3-algebra with a Lorentzian bi-invariant metric starting from an arbitrary semi-simple Lie algebra. The structure constants f^{ABCD} can be used to write down a maximally superconformal 3d theory that incorporates the expected degrees of freedom of multiple M2 branes, including the "center-of-mass" mode described by free scalar and fermion fields. The gauge field sector reduces to a three dimensional BF term, which underlies the gauge symmetry of the theory. We comment on the issue of unitarity of the quantum theory, which is problematic, despite the fact that the specific form of the interactions prevent the ghost fields from running in the internal lines of any Feynman diagram. Giving an expectation value to one of the scalar fields leads to the maximally supersymmetric 3d Yang-Mills Lagrangian with the addition of two U(1) multiplets, one of them ghost-like, which is decoupled at large g_YM.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1a1ae1708dd011b81f0895127b81fb5c5e6154fc

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Citations in the corpus

(1,0) superconformal models in six dimensions (2011, background): “This somewhat reminds the situation for the three-dimensional BLG theories [3, 4] with Lorentzian threealgebra [44, 45, 46, 47, 48], and certainly requires further investigation.”
N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds (2008, unknown): “Contents”
Generalized conformal symmetry and recovery of SO(8) in multiple M2 and D2 branes (2008, background): “An earlier proposal of L-BLG [3, 4, 5] has the desired symmetries, SO(8) and superconformal symmetries but there are several problems.”
n-ary algebras: a review with applications (2010, background): “As for the Lorentzian theory in [32], it can be recast as an ordinary gauge theory, but the Lie algebra associated with the FA is no longer semisimple, with its Levi factor given by the original semisimple g; as a result, the theory has features reminiscent of those of WZW models [279] and gauge the”
Ghost-free superconformal action for multiple M2-branes (2008, methodology): “In this paper we propose modifying the construction in [11, 12, 13] by gauging certain global symmetries.”
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.”
M2 to D2 revisited (2008, background): “When we have almost finished the paper, there appeared a paper [29] which overlaps considerably on the first proposal of this paper for deriving D2 from M2 in the BLG model.”
On type IIA Penrose limit and = 6 Chern-Simons theories (2008, background): “If we allow the non-degenerate metric, we can find N = 8 supersymmetric theories where we can take the number of branes N arbitrary large [22, 23, 24, 34, 35, 38, 41].”