N = 6 superconformal Chern-Simons theory was proposed as gauge theory dual to Type IIA string theory on AdS4*CP3. We study integrability of the theory from conformal dimension spectrum of single trace operators at planar limit. At strong `t Hooft coupling, the spectrum is obtained from excitation energy of free superstring on OSp(6|2,2)/SO(3,1)xSU(3)xU(1) supercoset. We recall that the worldsheet theory is integrable classically by utilizing well-known results concerning sigma model on symmetric space. With R-symmetry group SU(4), we also solve relevant Yang-Baxter equation for a spin chain system associated with the single trace operators. From the solution, we construct alternating spin chain Hamiltonian involving three-site interactions between 4 and 4*. At weak `t Hooft coupling, we study gauge theory perturbatively, and calculate action of dilatation operator to single trace operators up to two loops. To ensure consistency, we computed all relevant Feynman diagrams contributing to the dilatation opeator. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from Yang-Baxter equation. We further study new issues arising from the shortest gauge invariant operators transforming as 15 and 1 under SU(4). We observe that `wrapping interactions' are present, compute the true spectrum and find that the spectrum agrees with prediction from supersymmetry. We also find that scaling dimension computed naively from alternating spin chain Hamiltonian coincides with the true spectrum. We solve Bethe ansatz equations for small number of excitations, and find indications of correlation between excitations of 4's and 4*'s and of nonexistence of mesonic (4 4*) bound-state.
In this work we study some properties of the three dimensional $U(N)$ SUSY Chern-Simons coupled to a scalar field in the fundamental representation in the large $N$ limit. For large $N$ we show that the theory has two phases, one which is conformally invariant, and other where the superconformal symmetry is broken and masses for the matter fields are generated.
We compute superconformal indices for $\mathcal{N} = 3$ $\hat{ADE}$ Chern-Simons quiver gauge theories with a product gauge group $\prod_i U(N)_i$, using the method of supersymmetric localization. We also perform a large $N$ analysis of the index. This index includes contribution from non zero magnetic flux sector. The fact that these theories have a weakly coupled UV completion in terms of $\mathcal{N}= 3$ supersymmetric Chern-Simons Yang-Mills theories enables us to apply the localization technique. Such theories have dual M-theory description on $\mathrm{AdS}_4\times M_7$, where $M_7$ is a …
We present an explicit expression for the grand potential of the U(N)^3 superconformal Chern-Simons theory with the Chern-Simons levels being (k,0,-k). From the viewpoint of the Newton polygon, it is expected that the grand potential is given by the free energy of the topological string theory on the local D_5 del Pezzo geometry, though the explicit identification was a puzzle for years. We show how the expectation is realized explicitly. As a bonus, we can also study the Z_2 orbifold of this theory and find the grand potential is now given in terms of the local E_7 del Pezzo geometry.
We consider the partition function of the superconformal Chern-Simons theories with the quiver diagram being the affine D-type Dynkin diagram. Rewriting the partition function into that of a Fermi gas system, we show that the perturbative expansions in 1/N are summed up to an Airy function, as in the ABJM theory or more generally the theories of the affine A-type quiver. As a corollary, this provides a proof for the previous proposal in the large N limit. For special values of the Chern-Simons levels, we further identify three species of the membrane instantons and also conjecture an exact exp…
We study the large-$N$ limit of superconformal index for two strongly interacting Chern-Simons theories in three dimensions with $\mathcal{N}=2$ supersymmetry, and compare the result against the AdS/CFT dual, namely the data of full Kaluza-Klein reduction spectra obtained using the exceptional field theory technique. The two theories of interest are mABJM and GJV theories, which are obtained as IR fixed point of RG whose UV description is ABJM and maximally supersymmetric Yang-Mills theory respectively. We confirm agreement and the duality persists. For the case of mABJM it turns out that we n…
We study the partition function of three-dimensional ${\mathcal N}=4$ superconformal Chern-Simons theories of the circular quiver type, which are natural generalizations of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was known that the perturbative part of the partition function sums up to the Airy function as $Z(N)=e^{A}C^{-1/3}\mathrm{Ai}[C^{-1/3}(N-B)]$ with coefficients $C$, $B$ and $A$ and that for the non-perturbative part the divergences coming from the coefficients of worldsheet instantons and membrane instantons cancel among themselves. We find that many…
In the so-called (2,2) theory, which is the U(N)^4 circular quiver superconformal Chern-Simons theory with levels (k,0,-k,0), it was known that the instanton effects are described by the free energy of topological strings whose Gopakumar-Vafa invariants coincide with those of the local D_5 del Pezzo geometry. By considering two types of one-parameter rank deformations U(N) x U(N+M) x U(N+2M) x U(N+M) and U(N+M) x U(N) x U(N+M) x U(N), we classify the known diagonal BPS indices by degrees. Together with other two types of one-parameter deformations, we further propose the topological string exp…
It was known that the ABJM matrix model is dual to the topological string theory on a Calabi-Yau manifold. Using this relation it was possible to write down the exact instanton expansion of the partition function of the ABJM matrix model. The expression consists of a universal function constructed from the free energy of the refined topological string theory with an overall topological invariant characterizing the Calabi-Yau manifold. In this paper we explore two other superconformal Chern-Simons theories of the circular quiver type. We find that the partition function of one theory enjoys the…
We investigate the large $N$ instanton effects of partition functions in a class of $\mathcal{N}=4$ circular quiver Chern-Simons theories on a three-sphere. Our analysis is based on the supersymmetry localization and the Fermi-gas formalism. The resulting matrix model can be regarded as a two-parameter deformation of the ABJM matrix model, and has richer non-perturbative structures. Based on a systematic semi-classical analysis, we find analytic expressions of membrane instanton corrections. We also exactly compute the partition function for various cases and find some exact forms of worldshee…
In this article it is studied the 3-brane world in the context of five-dimensional Einstein-Chern-Simons gravity. We started by considering Israel's junction condition for AdS-Chern-Simons gravity. Using the S-expansion procedure, we mapped the AdS-Chern-Simons junction conditions to Einstein-Chern-Simons gravity, allowing us to derive effective four-dimensional Einstein-Chern-Simons field equations.
Squashing Gravity Dual of N=6 Superconformal Chern-Simons Gauge Theory
在11维超引力中，确定了商七球尺寸和挤压参数扰动下的四维场方程。商七球是CP^3上的S^1-丛，它被认为是基S^4上的S^2-纤维化。通过分析AdS 4超引力纯量势，得到了从N=1（或N=0）SO（5）x U（1）不变UV不动点到N=6（或N=0）SU（4）_R x U（1）不变IR不动点的全息超对称（或非超对称）重整化群（RG）流。三维边界理论描述的超共形陈-西蒙斯物质理论和一个对偶算子对应的RG流。
Dual conformal symmetry and Yangian symmetry are symmetries of amplitudes that have aided the study of scattering amplitudes in highly supersymmetric theories like ${\cal N}=4$ SYM and ABJM. However, in general such symmetries are absent from the theories with lesser or no supersymmetry. In this paper, we show that the tree level $2\to 2$ scattering amplitude in the 3d ${\cal N}=2$ Chern-Simons theory coupled to a fundamental chiral multiplet is dual superconformal invariant. In the 't Hooft large $N$ limit, the $2\to 2$ scattering amplitude in this theory has been shown to be tree-level exact…
