Comments on the Bagger-Lambert theory and multiple M2-branes

By Mark Van Raamsdonk. 2008

313 citations recorded by the source corpus.

We study the SO(8) superconformal theory proposed recently by Bagger and Lambert as a possible worldvolume theory for multiple M2-branes. For their explicit example with gauge group SO(4), we rewrite the theory (originally formulated in terms of a three-algebra) as an ordinary SU(2) × SU(2) gauge theory with bifundamental matter. In this description, the parity invariance of the theory, required for a proper description of M2-branes, is clarified. We describe the subspace of scalar field configurations on which the potential vanishes, correcting an earlier claim. Finally, we point out, for general three-algebras, a difficulty in constructing the required set of superconformal primary operators which should be present in the correct theory describing multiple M2-branes.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e1f7ed970750d96d677ae6da592a96921cc8d1b4

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In Astronomy and Astrophysics

1. S. Giombi
2. Xi Yin
3. O. Aharony
4. J. Maldacena
5. I. Klebanov
6. D. Jafferis
7. D. Gaiotto
8. Alberto Zaffaroni

In Nuclear and High Energy Physics

1. S. Giombi
2. Alberto Zaffaroni
3. D. Jafferis
4. I. Klebanov
5. Marcos Mariño
6. F. Benini
7. Xi Yin
8. J. Maldacena

In Statistical and Nonlinear Physics

1. S. Giombi
2. D. Gaiotto
3. D. Jafferis
4. Xi Yin
5. Alberto Zaffaroni
6. I. Klebanov
7. Marcos Mariño
8. O. Aharony

Citations in the corpus

• Lie 3-Algebra and Multiple M2-branes (2008, background): “Later it was realized that [30, 31, 32] the moduli space for the model with the A4 algebra does not match with the moduli space for 2 M2-branes in flat space, but rather it matches with the moduli space for an orbifold.”
• 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.”
• Superconformal Chern-Simons Theories and AdS(4)/CFT(3) Correspondence (2008, background): “4 ABJM U(N)2 gauge theory in superspace 7”
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals (2008, background): “In fact, one can show that our SU(2) × SU(2) (or (SU(2) × SU(2))/Z2) theory is precisely the same as that of [2] (which was written as a Chern-Simons-matter theory in [9]).”
• Exact correlators of BPS Operators from the 3d superconformal bootstrap (2014, background): “Explicit examples of (inequivalent) known N = 8 SCFTs are the U(N)k × U(N)−k ABJM theory when the Chern-Simons level is k = 1 or 2 [52], the U(N + 1)2 × U(N)−2 ABJ theory [53], and the SU(2)k × SU(2)−k BLG theories [54–59].”
• Scattering in three dimensions from rational maps (2013, background): “Moreover, color-ordered amplitudes in ABJM theory are invariant under cyclic permutations in even/odd sector (BLG theory with N = 8 can be viewed as a special case of ABJM for the gauge group SU(2)× SU(2) [15], and the color-ordered amplitudes in BLG can be obtained from those in ABJM).”
• D-brane charges in gravitational duals of 2 + 1 dimensional gauge theories and duality cascades (2009, background): “In the N = 3 case, which (for some values of N and M) flows to an N = 6 supersymmetric Chern-Simons-matter theory in the IR, we argue that the careful analysis of the charges leads to a shift in the value of the B2 field in the IR solution by 1/2, in units where its periodicity is one, compared to…”
• Selfdual strings and loop space Nahm equations (2008, background): “10 Now, as the only case where an action can be written down is for SO(4), we can also rely on the relation SO(4) = SU(2)× SU(2) and write the BaggerLambert action as a usual gauge theory in terms of a two SU(2) gauge fields as in [18], [19].”
• N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets (2008, background): “It is parity even [10, 11] and its superconformal symmetry group is OSp(8|4).”
• Tilings, Chern-Simons Theories and M2 Branes (2008, background): “The theory constructed in [13] is the conclusion of a long activity that followed the discovery of the BGL N = 8 supersymmetric Chern-Simons theory and the attempts to interpret and generalize it [14, 15, 16].”