Superconformal Chern-Simons Matter Theory Research Articles

Identification of bulk coupling constant in higher spin/ABJ correspondence

We study the conjectured duality between the $\mathcal{N}=6$ Vasiliev higher spin theory on $AdS_4$ and 3d $\mathcal{N}=6$ superconformal Chern-Simons matter theory known as the ABJ theory. We discuss how the parameters in the ABJ theory should be related to the bulk coupling constant in the Vasiliev theory. For this purpose, we compute two-point function of stress tensor in the ABJ theory by using supersymmmetry localization. Our result justifies the proposal by arXiv:1504.00365 and determine the unknown coefficient in the previous work.

Exact results on ABJ theory and the refined topological string

We study the partition function of the ABJ theory, which is the N=6 superconformal Chern-Simons matter theory with gauge group U(N)xU(N+M) and Chern-Simons levels (k,-k). We exactly compute the ABJ partition function on a three sphere for various k, M and N via the Fermi gas approach. By using these exact data, we show that the ABJ partition function is completely determined by the refined topological string on local P^1 x P^1, including membrane instanton effects in the M-theory dual.

Direct derivation of “mirror” ABJ partition function

We study the partition function of the three-dimensional N=6 U(N)_k x U(N+M)_{-k} superconformal Chern-Simons matter theory known as the ABJ theory. We prove that the ABJ partition function on S^3 is exactly the same as a formula recently proposed by Awata, Hirano and Shigemori. While this formula was previously obtained by an analytic continuation from the L(2,1) lens space matrix model, we directly derive this by using a generalization of the Cauchy determinant identity. We also give an interpretation for the formula from brane picture.

Construction of new D = 3, $ \mathcal{N}=4 $ quiver gauge theories

In this paper we propose a special class of 3-algebras, called double-symplectic 3-algebras. We further show that a consistent contraction of the double-symplectic 3-algebra gives a new 3-algebra, called an N=4 three-algebra, which is then identified as the exact gauged three-algebra in the N=4 quiver gauge theories. A systematic construction is proposed for the 3-brackets and fundamental identities used in building up the N=4 theories, by starting with two superalgebras whose bosonic parts share at least one simple factor or U(1) factor. This leads to a systematic way of constructing D=3, N=4 quiver theories, of which several examples with new gauge groups are presented in detail. The general N=4 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be also re-derived in our new 3-algebra approach.

Topologically gauged superconformal Chern-Simons matter theories

By coupling $ \mathcal{N}=8 $ superconformal matter to $ \mathcal{N}=8 $ superconformal Chern-Simons gravity in three dimensions we obtain theories with novel terms in the scalar potential leading to AdS 3 solutions and superconformal symmetry breaking. If we start from the theory derived by Bagger, Lambert and Gustavsson, our coupled theory either inherits the SO(4) gauge group or reduces it to SO(3). If the construction is instead based on a free matter theory we find that the gravitational topological gauging also requires the introduction of a Chern-Simons gauge sector resulting in a consistent theory for any SO(N ) gauge group.

Covariantly constant curvature tensors andD=3,N=4, 5, 8 Chern-Simons matter theories

We construct some examples of $D=3$, $\mathcal{N}=4$ GW theory and $\mathcal{N}=5$ superconformal Chern-Simons matter theory by using the covariantly constant curvature of a quaternionic-Kahler manifold to construct the symplectic 3-algebra in the theories. Comparing with the previous theories, the $\mathcal{N}=4$, 5 theories constructed in this way possess a local $Sp(2n)$ symmetry and a diffeomorphism symmetry associated with the quaternionic-Kahler manifold. We also construct a generalized $\mathcal{N}=8$ BLG theory by utilizing the dual curvature operator of a maximally symmetric space of dimension 4 to construct the Nambu 3-algebra. Comparing with the previous $\mathcal{N}=8$ BLG theory, the theory has a diffeomorphism invariance and a local $SO(4)$ invariance associated with the symmetric space.

Superspace formulation in a three-algebra approach toD=3,N=4, 5 superconformal Chern-Simons matter theories

We present a superspace formulation of the D=3, N=4,5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action, and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new super-potential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4,5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be rederived in our 3-algebra approach. All known N=4,5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie-algebra realization of symplectic 3-algebras.

Holographic supersymmetric membrane flows

The M-theory lift of SU(3) × U(1)R-invariant RG flow via a combinatorical use of the four-dimensional flow and 11-dimensional Einstein–Maxwell equations was found previously. By taking the three internal coordinates differently and preserving only the SU(3) symmetry from the CP2 space, we find a new 11-dimensional solution of the SU(3)-invariant RG flow interpolating from the SO(8)-invariant UV fixed point to the SU(3) × U(1)R-invariant IR fixed point in four dimensions. We describe how the corresponding three-dimensional superconformal Chern–Simons matter theory deforms. By replacing the above CP2 space with the Einstein–Kahler twofold, we also find out a new 11-dimensional solution of the SU(2) × U(1)-invariant RG flow connecting the above two fixed points in four dimensions.

ARE THERE ANY NEW VACUA OF GAUGED ${\mathcal N}=8$ SUPERGRAVITY IN FOUR DIMENSIONS?

We consider the most general SU(3) singlet space of gauged [Formula: see text] supergravity in four dimensions. The SU(3)-invariant six scalar fields in the theory can be viewed in terms of six real four-forms. By exponentiating these four-forms, we eventually obtain the new scalar potential. For the two extreme limits, we reproduce the previous results found by Warner in 1983. In particular, for the [Formula: see text] critical point, we find the constraint surface parametrized by three scalar fields on which the cosmological constant has the same value. We obtain the BPS domain-wall solutions for restricted scalar submanifold. We also describe the three-dimensional mass-deformed superconformal Chern–Simons matter theory dual to the above supersymmetric flows in four dimensions.

M2-BRANES AND AdS/CFT

We provide a brief introduction to the ABJM theory, the level kU(N) × U(N) superconformal Chern-Simons matter theory which has been conjectured to describe N coincident M2 -branes. We discuss its dual formulation in terms of M -theory on AdS4 × S7/ℤk and review some of the evidence in favor of the conjecture. We end with a brief discussion of the important role played by the monopole operators.

The gauge dual of a warped product of AdS4 and a squashed and stretched seven-manifold

Corrado, Pilch and Warner found in 2001 the second 11-dimensional solution where the deformed geometry of S7 in the lift contains S2 × S2. We identify the gauge dual of this background with the theory described by Franco, Klebanov and Rodriguez-Gomez recently. It is the U(N) × U(N) × U(N) gauge theory with two SU(2) doublet chiral fields B1 transforming in the , B2 transforming in the , C1 in the and C2 in the as well as an adjoint field Φ in the (1, adj, 1) representation. By adding the mass term for adjoint field Φ, the detailed correspondence between fields of AdS4 supergravity and composite operators of the IR field theory is determined. Moreover, we compute the spin-2 KK modes around a warped product of AdS4 and a squashed and stretched seven-manifold. This background with global SU(2) × SU(2) × U(1)R symmetry is related to a U(N) × U(N) × U(N) superconformal Chern–Simons matter theory with eighth-order superpotential and Chern–Simons level (1, 1, −2). The mass-squared in AdS4 depends on SU(2) × SU(2) × U(1)R quantum numbers and the KK excitation number. The dimensions of spin-2 operators are found.

Perturbing around a warped product ofAdS4and seven-ellipsoid

We compute the spin-2 Kaluza-Klein modes around a warped product of AdS_4 and a seven-ellipsoid. This background with global G_2 symmetry is related to a U(N) x U(N) N=1 superconformal Chern-Simons matter theory with sixth order superpotential. The mass-squared in AdS_4 is quadratic in G_2 quantum number and KK excitation number. We determine the dimensions of spin-2 operators using the AdS/CFT correspondence. The connection to N=2 theory preserving SU(3) x U(1)_R is also discussed.

Marginal deformations and 3-algebra structures

We study marginal deformations of superconformal Chern–Simons matter theories that are based on 3-algebras. For this, we introduce the notion of an associated 3-product, which captures very general gauge invariant deformations of the superpotentials of the BLG and ABJM models. We also consider conformal multi-trace deformations preserving N = 2 supersymmetry. We then use N = 2 supergraph techniques to compute the two-loop beta functions of these deformations. Besides confirming conformal invariance of both the BLG and ABJM models, we also verify that the recently proposed β-deformations of the ABJM model are indeed marginal to the order we are considering.

Squashing gravity dual of superconformal Chern–Simons gauge theory

Four-dimensional field equations are determined for perturbations of the quotient 7-sphere size and squashing parameter in 11-dimensional supergravity. The quotient 7-sphere is an S1-bundle over the CP3 which is regarded as an S2-fibration over the base S4. By analyzing the AdS 4 supergravity scalar potential, the holographic supersymmetric (or nonsupersymmetric) renormalization group (RG) flow from (or ) SO(5) × U(1)-invariant UV fixed point to (or ) SU(4)R × U(1)-invariant IR fixed point is obtained. The three-dimensional boundary theories are described by superconformal Chern–Simons matter theories and a dual operator corresponding to this RG flow is described.

Other squashing deformation and [formula omitted] superconformal Chern–Simons gauge theory

We consider one of the well-known solutions in eleven-dimensional supergravity where the seven-dimensional Einstein space is given by a SO(3)-bundle over the CP2. By reexamining the AdS4 supergravity scalar potential, the holographic renormalization group flow from N=(0,1)SU(3)×SU(2)-invariant UV fixed point to N=(3,0)SU(3)×SU(2)-invariant IR fixed point is reinterpreted. A dual operator in three-dimensional superconformal Chern–Simons matter theories corresponding to this RG flow is described.