On the Moduli Space of Elliptic Maxwell-Chern-Simons Theories

By Y. Imamura, Keisuke Kimura. 2008

183 citations recorded by the source corpus.

We analyze the moduli space of the low-energy limit of 3-dimensional N = 3 MaxwellChern-Simons theories described by circular quiver diagrams, as for 4-dimensional elliptic models. We define the theories by using D3-NS5-(k,1)5-brane systems with an arbitrary number of fivebranes. The supersymmetry is expected to be enhanced to N =4i n the low-energy limit. We show that the Higgs branch, in which all bifundamental scalar fields develop vacuum expectation values, is an abelian orbifold of C 4 . We confirm that the same geometry is obtained as an M-theory dual of the brane system. We also consider theories realized by introducing more than two kinds of fivebranes, and obtain nontoric fourfolds as moduli spaces. Recently, there has been great interest in 3-dimensional superconformal field theories as theories for describing multiple M2-branes in various backgrounds. This was triggered by the proposal of a new class of 3-dimensional theories by Bagger and Lambert, 1)–3) and Gusstavson. 4),5) The model (BLG model) possesses N(d=3) =8 superconformal symmetry and is based on Lie 3-algebra. The action of the BLG model includes the structure constant f abc d of a Lie 3-algebra, which determines the form of the interactions, and a metric h ab , which appears in the coefficients of the kinetic terms. These tensors must satisfy certain conditions required by the supersymmetry invariance of the action. If these tensors satisfy the conditions, we can write down the action of a BLG model. The constraint imposed on the structure constant is called a fundamental identity. It was soon realized that the identity is very restrictive, 6) and it was proved that if we assume that the metric is positive definite and the algebra is finite dimensional, there is only one nontrivial Lie 3-algebra, 7),8) which is called an A4 algebra. The BLG model based on the A4 algebra is a SU(2)×SU(2) Chern-Simons theory with levels k and −k for each SU(2) factor. Analysis of this model showed that it describes a pair of M2-branes in certain orbifold backgrounds. 9)–11) As a theory for an arbitrary number of M2-branes, a model based on an algebra with a Lorenzian metric was proposed in Refs. 12)– 14). Because of the indefinite metric, the model includes unwanted ghost modes. Although the ghost modes can be removed by treating them as background fields satisfying classical equations of motion, 14),15) or by gauging certain symmetries and fixing them, 16),17) this procedure breaks the conformal invariance, and the theory becomes D2-brane theory 14),16),18) by the mechanism proposed in Ref. 19) unless the

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

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Citations in the corpus

Chiral flavors and M2-branes at toric CY4 singularities (2009, background): “If N ≥ 3, H7 is 3-Sasakian and hyper-Kähler geometry can be used to construct dual pairs [2, 3, 4, 5, 6].”
Towards the F-theorem: $ \mathcal{N} = 2 $ field theories on the three-sphere (2011, methodology): “In section 3 we discuss an infinite class of the necklace quiver gauge theories with N = 2 supersymmetry where the N = 3 models proposed in [25, 26], and studied in [10], are deformed by adding a cubic superpotential for the adjoints [27].”
The large N limit of quiver matrix models and Sasaki-Einstein manifolds (2011, result): “More recently in [7] and [8] similar results have been obtained for classes of N = 3 Chern-Simons-quivers [9] with M-theory duals of the form AdS4× Y , where Y are tri-Sasakian manifolds [10].”
ABJM theory as a Fermi gas (2011, methodology): “We will set up the formalism for the necklace quivers with r nodes considered in [38, 39], and with fundamental matter in each node (see figure 2).”
The gauge dual of Romans mass (2009, methodology): “Nevertheless, there is now an infinite series of N = 3 examples [19, 20], which can be derived using the same duality procedure as in [1].”
Localization techniques in quantum field theories (2016, background): “The reader can consult [3, 92, 105] for more details.”
Moduli spaces of Chern-Simons quiver gauge theories and AdS(4)/CFT(3) (2008, background): “A further quotient of this space6 by the relative U(1) gives the conifold singularity, which is of course the mesonic moduli space of the 4d theory [3].”
Multimatrix models and tri-Sasaki Einstein spaces (2010, methodology): “These models were introduced in [12] where their type IIB brane constructions were presented.”
Tilings, Chern-Simons Theories and M2 Branes (2008, methodology): “We will encounter some models that have already appeared in the literature as orbifold of the ABJM theory and may have enhanced N = 3 or N = 4 supersymmetry [17, 18, 20, 21, 23], as well as many other new models based on 3+1 dimensional quivers.”
Lifshitz spacetimes from AdS null and cosmological solutions (2010, background): “Similarly we expect that the AdS4-deformed solutions are dual to appropriate lightlike deformations of Chern-Simons theories arising on M2-branes stacked at appropriate supersymmetric singularities [39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], dimensionally reduced along a compact direction.”
A simple class of N = 3 gauge/gravity duals (2008, methodology): “In section 3 we then engineer the theories in string theory (again as done in [19]); it”