Three-dimensional N=6 superconformal field theories and their membrane dynamics (original) (raw)
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Rings of short 𝒩 = 3 superfields in three dimensions and M-theory on AdS 4 × N 0,1,0
Classical and Quantum Gravity, 2001
In this paper we investigate three-dimensional superconformal gauge theories with N = 3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three dimensional N = 3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of N = 2 theories. When the superconformal field theory is realized on the world-volume of an M2-brane such superfield ring is the counterpart of the ring defined by the algebraic geometry of the 8-dimensional cone transverse to the brane. This and other arguments identify the N = 3 superconformal field theory dual to M-theory compactified on AdS 4 × N 0,1,0. It is an N = 3 gauge theory with SU(N) × SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern Simons interaction. The AdS/CFT correspondence can be directly verified using the recently worked out Kaluza Klein spectrum of N 0,1,0 and we find a perfect match. We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corresponding to certain massive KK modes are organized into a massive spin 3 2 N = 3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken N = 4 theory. We investigate this intriguing and inspiring feature in a separate paper.
Rings of short= 3 superfields in three dimensions and M-theory on AdS4× N0, 1, 0
In this paper we investigate three-dimensional superconformal gauge theories with N = 3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three dimensional N = 3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of N = 2 theories. When the superconformal field theory is realized on the world-volume of an M2-brane such superfield ring is the counterpart of the ring defined by the algebraic geometry of the 8-dimensional cone transverse to the brane. This and other arguments identify the N = 3 superconformal field theory dual to M-theory compactified on AdS 4 × N 0,1,0 . It is an N = 3 gauge theory with SU(N) × SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern Simons interaction. The AdS/CFT correspondence can be directly verified using the recently worked out Kaluza Klein spectrum of N 0,1,0 and we find a perfect match. We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corresponding to certain massive KK modes are organized into a massive spin 3 2 N = 3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken N = 4 theory. We investigate this intriguing and inspiring feature in a separate paper.
A non-supersymmetric large- N 3D CFT and its gravity dual
Journal of High Energy Physics, 2008
We propose a three dimensional non-supersymmetric theory that is conformal in the large N limit. In a certain well defined bosonic sub-sector of gauge invariant operators, this theory is planar equivalent to the theory recently proposed by Aharony, Bergman, Jafferis and Maldacena as the theory on multiple M2 branes at an orbifold singularity. We discuss the realization of the theory on a brane configuration of type 0B string theory. Moreover, we propose an 11D gravity dual, obtained by a projection of M-theory on AdS 4 × S 7 /Z k .
Journal of High Energy Physics, 2019
In the framework of six-dimensional conformal field theories with mathcalN=left(1,0right)\mathcal{N}=\left(1,\ 0\right)mathcalN=left(1,0right) N = 1 , 0 supersymmetry we develop the map between the holographic description, the field theoretical description and the associated Hanany-Witten set-ups. General expressions that calculate various observables are presented. The study of string solitons singles out a special background of Massive IIA on which we show (by explicitly finding a Lax pair) that the Neveu-Schwarz part of the string sigma model is classically integrable. We study the particular dual conformal field theory and compute some of its observables.
M-theory on the Stiefel manifold and 3d conformal field theories
Journal of High Energy Physics - J HIGH ENERGY PHYS, 2000
We compute the mass and multiplet spectrum of M-theory compactified on the product of AdS4 spacetime by the Stiefel manifold V(5,2) = SO(5)/SO(3), and we use this information to deduce via the AdS/CFT map the primary operator content of the boundary 𝒩 = 2 conformal field theory. We make an attempt for a candidate supersymmetric gauge theory that, at strong coupling, should be related to parallel M2-branes on the singular point of the non-compact Calabi-Yau four-fold ∑a = 15za2 = 0, describing the cone on V(5,2).
AdS 3 / CFT 2 correspondence and space-time N = 3 superconformal algebra
Journal of High Energy Physics, 1999
We study a Wess-Zumino-Witten model with target space AdS 3 ×(S 3 ×S 3 ×S 1)/Z 2. This allows us to construct space-time N = 3 superconformal theories. By combining left-, and right-moving parts through a GSO and a Z 2 projections, a new asymmetric (N , N) = (3, 1) model is obtained. It has an extra gauge (affine) SU (2) symmetry in the target space of the type IIA string. An associated configuration is realized as slantwise intersecting M5-M2 branes with a Z 2-fixed plane in the M-theory viewpoint.
We find the exact solution for a finite size Giant Magnon in the SU(2)×SU(2) sector of the string dual of the N = 6 superconformal Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. The finite size Giant Magnon solution consists of two magnons, one in each SU(2). In the infinite size limit this solution corresponds to the Giant Magnon solution of arXiv:0806.4959. The magnon dispersion relation exhibits finite-size exponential corrections with respect to the infinite size limit solution. 1 Introduction and summary Recently, motivated by the possible description of the worldvolume dynamics of coincident membranes in M-theory, a new class of conformal invariant, maximally supersymmetric field theories in 2+1 dimensions has been found [1, 2]. These theories contain gauge fields with Chern-Simons-like kinetic terms. Based on this development, Aharony, Bergman, Jafferis and Maldacena proposed a new gauge/string
Aspects of superconformal field theories in six dimensions
Journal of High Energy Physics, 2004
We introduce the analytic superspace formalism for six-dimensional (N, 0) superconformal field theories. Concentrating on the (2, 0) theory we write down the Ward identities for correlation functions in the theory and show how to solve them. We then consider the four-point function of four energy momentum multiplets in detail, explicitly solving the Ward identities in this case. We expand the four-point function using both Schur polynomials, which lead to a simple formula in terms of a single function of two variables, and (a supersymmetric generalisation of) Jack polynomials, which allow a conformal partial wave expansion. We then perform a complete conformal partial wave analysis of both the free theory four-point function and the AdS dual four-point function. We also discuss certain operators at the threshold of the series a) unitary bound, and prove that some such operators can not develop anomalous dimensions, by finding selection rules for certain three-point functions. For those operators which are not protected, we find representations with which they may combine to become long.
ABCD of 3d calN=8{\cal N}=8calN=8 and 4 Superconformal Field Theories
We argue the equivalence between the infrared conformal field theory of the 3d N = 8 supersymmetric Yang-Mills theories of ABCD (U (N ), SO(2N + 1), Sp(2N ), O(2N )) gauge groups and the ABJ(M) theories of U (N ) k × U (Ñ ) −k for k = 1, 2. We support this duality by comparing the superconformal index of the IR limit of these super Yang-Mills theories and that of those ABJ(M) models. Especially we find the match between two indices of (mirror dual of) the N = 8 U (N ) SYM and of U (N ) 1 × U (N ) −1 ABJM model. Also we take large N limit of ABCD super Yang-Mills theories with additional fundamental hyper-multiplets and infer the large N limit of N = 8 ABCD theories themselves, finding the expected gravitational duals. With the additional input on finite N, we argue the equivalence of Yang-Mills and ABJ(M) theories for all N. We further explore similar dualities to Chern-Simons matter theories for N = 4 Yang-Mills theories related by mirror symmetry.