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Bagger-Lambert Theory for General Lie Algebras · Around

2008

Bagger-Lambert Theory for General Lie Algebras

Gomis, Jaume, Milanesi, Giuseppe, Russo, Jorge G.

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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.

Built on

V.T. Filippov, “n-Lie algebras,” Sib. Mat. Zh., 26 No. 6, 126140 (1985)
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E. Witten, “(2+1)-Dimensional Gravity as an Exactly Soluble System,” Nucl. Phys. B 311
1988
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D. Bar-Natan and E. Witten, “Perturbative expansion of Chern-Simons theory with noncompact gauge group,” Commun. Math. Phys. 141
1991
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D. Birmingham, M. Blau, M. Rakowski and G. Thompson, “Topological field theory,” Phys. Rept. 209
1991
Earlier work this paper cites.

Similar

C. R. Nappi and E. Witten, “A WZW model based on a nonsemisimple group,” Phys. Rev. Lett. 71
1993
Cited alongside, same era.
A. A. Tseytlin, “On gauge theories for nonsemisimple groups,” Nucl. Phys. B 450
1995
Cited alongside, same era.
J. H. Schwarz, “Superconformal Chern-Simons theories,” JHEP 0411
2004
Cited alongside, same era.
A. Basu and J. A. Harvey, “The M2-M5 brane system and a generalized Nahm’s equation,” Nucl. Phys. B 713
2005
Cited alongside, same era.
A. Gustavsson, “Algebraic structures on parallel M2-branes,” arXiv:0709.1260 [hep-th]
Original
Cited in the paper.
G. Papadopoulos, “M2-branes, 3-Lie Algebras and Plucker relations,” arXiv:0804.2662 [hep-th]
Original
Cited in the paper.
J. P. Gauntlett and J. B. Gutowski, “Constraining Maximally Supersymmetric Membrane Actions,” arXiv:0804.3078 [hep-th]
Original
Cited in the paper.
A. Gustavsson, “Selfdual strings and loop space Nahm equations,” arXiv:0802.3456 [hep-th]
Original
Cited in the paper.
P. M. Ho, R. C. Hou and Y. Matsuo, “Lie 3-Algebra and Multiple M2-branes,” arXiv:0804.2110 [hep-th]
Original
Cited in the paper.
J. Figueroa-O’Farrill and G. Papadopoulos, “Pluecker-type relations for orthogonal planes,” arXiv:math/0211170
Cited in the paper.
U. Gran, B. E. W. Nilsson and C. Petersson, “On relating multiple M2 and D2-branes,” arXiv:0804.1784 [hep-th]
Original
Cited in the paper.
M. A. Bandres, A. E. Lipstein and J. H. Schwarz, “N = 8 Superconformal Chern–Simons Theories,” arXiv:0803.3242 [hep-th]
Original
Cited in the paper.

Then

J. Bagger and N. Lambert, “Modeling multiple M2’s,” Phys. Rev. D 75
2007
Later among the works it cites.
J. Bagger and N. Lambert, “Gauge Symmetry and Supersymmetry of Multiple M2-Branes,” Phys. Rev. D 77
Original
2008
Closest in time.
J. Bagger and N. Lambert, “Comments On Multiple M2-branes,” JHEP 0802
Original
2008
Closest in time.

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