Superconformal Chern-Simons theories

By J. Schwarz. 2004

423 citations recorded by the source corpus.

A Lagrangian description of a maximally supersymmetric conformal field theory in three dimensions was constructed recently by Bagger and Lambert (BL). The BL theory has SO(4) gauge symmetry and contains scalar and spinor fields that transform as 4-vectors. We verify that this theory has OSp(8|4) superconformal symmetry and that it is parity conserving despite the fact that it contains a Chern-Simons term. We describe several unsuccessful attempts to construct theories of this type for other gauge groups and representations. This experience leads us to conjecture the uniqueness of the BL theory. Given its large symmetry, we expect this theory to play a significant role in the future development of string theory and M-theory.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/81ddd3428be3f8a8d90bea5d4c8d592384239973

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In Mathematical Physics

1. D. Gaiotto
2. I. Klebanov
3. D. Jafferis
4. A. Tomasiello
5. E. Witten
6. S. Giombi
7. D. Martelli
8. Marcos Mariño

In Nuclear and High Energy Physics

1. Marcos Mariño
2. J. Maldacena
3. I. Klebanov
4. D. Gaiotto
5. S. Giombi
6. F. Benini
7. D. Jafferis
8. T. Takayanagi

Citations in the corpus

• Comments on the Bagger-Lambert theory and multiple M2-branes (2008, methodology): “Invariance of the full action presumably now follows from supersymmetry, however we refer the reader to [ 10 ] for a more explicit discussion of parity for the fermionic terms in the action.”
• Exact results for Wilson loops in superconformal Chern-Simons theories with matter (2009, methodology): “Setup The class of theories we will be considering, N = 2 supersymmetric Chern-Simons theory with matter, are described in [5] for Minkowski space.”
• A Massive Study of M2-brane Proposals (2008, background): “from the point of view of the worldvolume of the M2-branes [25] (for another precursor see [46]).”
• Superconformal Chern-Simons Theories and AdS(4)/CFT(3) Correspondence (2008, background): “He found conventional Chern-Simons terms for each of the SU(2) gauge fields although with opposite signs, as noted already in [7].”
• Superstrings on AdS4 × ℂℙ3 as a coset sigma-model (2008, background): “nnection 14 4.2 κ-variations of the Lax connection 15 5. Plane-wave limit 16 A. Gamma- and T-matrices 22 B. Parametrizations of CP3 24 1. Introduction and Summary Superconformal Chern-Simons theories [1] conjectured to describe the low-energy world-volume dynamics of multiple M2-branes are receiving”
• d = 3 bosonic vector models coupled to Chern-Simons gauge theories (2011, background): “The action of the N = 2 theory [26, 27], after integrating out all the auxiliary fields, is”
• Spin Chains in N = 6 Superconformal Chern-Simons-Matter Theory (2008, background): “The dual gauge theory is a special case of the N = 3 superconformal Chern-Simons-matter (CSM) theories studied in [10] (see [11, 12, 13, 14, 15] for earlier works), which has quiver type matter content and enhanced N = 6 supersymmetry.”
• Supersymmetric AdS(4) compactifications of IIA supergravity (2004, background): “This theory is expected to admit a three-dimensional conformal field theory dual, see [39] for a recent discussion and [40] for earlier work on this subject.”
• Fractional M2-branes (2008, background): “Motivated by the work of Bagger and Lambert [1] (see also [2-4]), there has recently been great interest in studying three dimensional superconformal field theories and their relation to the low-energy theory on M2-branes.”
• Charges of monopole operators in Chern-Simons Yang-Mills theory (2009, methodology): “Requiring manifest unitarity restricts the gauge group to SO(4) [6,7]; this model may be reformulated as SU(2)×SU(2) gauge theory with conventional Chern-Simons terms having opposite levels k and −k [8,9].”
• Notes on superconformal Chern-Simons-Matter theories (2007, background): “It was pointed out in [16] that supersymmetric Chern-Simons theories, which are by themselves topological but may be coupled to matter fields that carry physical degrees of freedom, give rise to a natural class of classically conformal theories.”
• Generalized conformal symmetry and recovery of SO(8) in multiple M2 and D2 branes (2008, background): “They generalized the superconformal Chern-Simons matter theories [17, 18] to the N = 6 superconformal U(N)×U(N) theories.”
• The large N limit of quiver matrix models and Sasaki-Einstein manifolds (2011, background): “Earlier foundational work on this topic includes [27, 3, 28].”
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals (2008, background): “Conformal Chern-Simons theories were explored in [1] for this purpose, but these theories did not have enough supersymmetry.”
• N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets (2008, background): “For the conformal theory of M2 branes, one needs more supersymmetry [9] and the recent works related to the BL theory and the GW theory can be regarded as concrete steps toward this direction.”