N = 8 Superconformal Chern--Simons Theories

By Miguel Ángel Gracia Bandrés, A. Lipstein, J. Schwarz. 2008

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

View Paper: https://www.semanticscholar.org/paper/c207bfa8cce7f95b1dbf78aff1250f996b226498

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Y. Imamura
2. K. Zarembo
3. I. Klebanov
4. Mark Van Raamsdonk
5. A. Tseytlin
6. J. A. Azcárraga
7. J. M. Izquierdo
8. Kimyeong Lee

In Nuclear and High Energy Physics

1. Y. Imamura
2. J. A. Azcárraga
3. J. M. Izquierdo
4. A. Tseytlin
5. I. Klebanov
6. S. Giombi
7. S. Frolov
8. K. Zarembo

In Statistical and Nonlinear Physics

1. J. A. Azcárraga
2. J. M. Izquierdo
3. Y. Imamura
4. Yutaka Matsuo
5. Pei-Ming Ho
6. I. Klebanov
7. Mark Van Raamsdonk
8. K. Zarembo

Citations in the corpus

• Ghost-free superconformal action for multiple M2-branes (2008, background): “Its full superconformal symmetry was verified in [6], which also conjectured its uniqueness.”
• Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry (2008, methodology): “This theory is parity conserving and has SO(4) = SU(2) × SU(2) gauge symmetry [23, 24].”
• 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).”
• 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].”
• N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds (2008, background): “The SO(4) BLG theory can be rewritten as an ordinary gauge theory [7, 8].”
• Comments on the Bagger-Lambert theory and multiple M2-branes (2008, background): “Note: After this work was completed, the papers [10, 11, 12] appeared, which have some overlap with the present work.”
• n-ary algebras: a review with applications (2010, background): “The relative minus sign in Ω+ − Ω− solves the problem of parity invariance [302], since the odd parity of the standard CS term is compensated by requiring that parity interchanges the two different SU(2) gauge fields so that H+ ↔ H−, something that could not be done if the CS term were the single on”
• Bagger-Lambert Theory for General Lie Algebras (2008, unknown): “Full superconformal invariance was proven in [17].”
• M2-branes, 3-Lie algebras and Plucker relations (2008, background): “1) has more solutions than those given in [2], see also [16].”