3D superconformal theories from Sasakian seven-manifolds: new non-trivial evidences for AdS 4/CFT 3 (original) (raw)
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Notes on toric Sasaki-Einstein seven-manifolds and AdS4/CFT3
Journal of High Energy Physics
We study the geometry and topology of two infinite families Yp,k of Sasaki-Einstein seven-manifolds, that are expected to be AdS4/CFT3 dual to families of = 2 superconformal field theories in three dimensions. These manifolds, labelled by two positive integers p and k, are Lens space bundles S3/p over P2 and P1 × P1, respectively. The corresponding Calabi-Yau cones are toric. We present their toric diagrams and gauged linear sigma model charges in terms of p and k, and find that the Yp,k manifolds interpolate between certain orbifolds of the homogeneous spaces S7,M3,2 and Q1,1,1.
M-theory and seven-dimensional inhomogeneous Sasaki-Einstein manifolds
Journal of High Energy Physics, 2011
Seven-dimensional inhomogeneous Sasaki-Einstein manifolds Y p,k (KE 4 ) present a challenging example of AdS/CFT correspondence. At present, their field theory duals for KE 4 = CP 2 base are proposed only within a restricted range 3p/2 ≤ k ≤ 2p as N = 2 quiver Chern-Simons-matter theories with SU (N ) × SU (N ) × SU (N ) gauge group, nine bifundamental chiral multiplets interacting through a cubic superpotential. To further elucidate this correspondence, we use particle approximation both at classical and quantum level. We setup a concrete AdS/CFT mapping of conserved quantities using geodesic motions, and turn to solutions of scalar Laplace equation in Y p,k . The eigenmodes also provide an interesting subset of Kaluza-Klein spectrum for D = 11 supergravity in AdS 4 ×Y p,k , and are dual to protected operators written in terms of matter multiplets in the dual conformal field theory.
Classical and Quantum Gravity, 2000
In this paper we fill a necessary gap in order to realize the explicit comparison between the Kaluza Klein spectra of supergravity compactified on AdS 4 × X 7 and superconformal field theories living on the world volume of M2-branes. On the algebraic side we consider the superalgebra Osp(N |4) and we study the double intepretation of its unitary irreducible representations either as supermultiplets of particle states in the bulk or as conformal superfield on the boundary. On the lagrangian field theory side we construct, using rheonomy rather than superfield techniques, the generic form of an N = 2, d = 3 gauge theory. Indeed the superconformal multiplets are supposed to be composite operators in a suitable gauge theory.
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.
𝒩 = 8 superconformal gauge theories and M 2 branes
Journal of High Energy Physics, 2009
Based on recent developments, in this letter we find 2 + 1 dimensional gauge theories with scale invariance and N = 8 supersymmetry. The gauge theories are defined by a lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. The theories are parity invariant and do not admit any tunable coupling constant. In the case of SU(N) the moduli space of vacua contains a branch of the form (R 8) N /S N. These properties are expected for the field theory living on a stack of M2 branes.
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.
Toric Geometry, Sasaki–Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
Communications in Mathematical Physics, 2006
Recently an infinite family of explicit Sasaki-Einstein metrics Y p,q on S 2 × S 3 has been discovered, where p and q are two coprime positive integers, with q < p. These give rise to a corresponding family of Calabi-Yau cones, which moreover are toric. Aided by several recent results in toric geometry, we show that these are Kähler quotients C 4 //U (1), namely the vacua of gauged linear sigma models with charges (p, p, −p + q, −p − q), thereby generalising the conifold, which is p = 1, q = 0. We present the corresponding toric diagrams and show that these may be embedded in the toric diagram for the orbifold C 3 /Z p+1 × Z p+1 for all q < p with fixed p. We hence find that the Y p,q manifolds are AdS/CFT dual to an infinite class of N = 1 superconformal field theories arising as IR fixed points of toric quiver gauge theories with gauge group SU (N ) 2p . As a non-trivial example, we show that Y 2,1 is an explicit irregular Sasaki-Einstein metric on the horizon of the complex cone over the first del Pezzo surface. The dual quiver gauge theory has already been constructed for this case and hence we can predict the exact central charge of this theory at its IR fixed point using the AdS/CFT correspondence. The value we obtain is a quadratic irrational number and, remarkably, agrees with a recent purely field theoretic calculation using a-maximisation.
Supersymmetric AdS backgrounds in string and M-theory
To appear in the proceedings of, 2004
We first present a short review of general supersymmetric compactifications in string and M-theory using the language of G-structures and intrinsic torsion. We then summarize recent work on the generic conditions for supersymmetric AdS 5 backgrounds in M-theory and the construction of classes of new solutions. Turning to AdS 5 compactifications in type IIB, we summarize the construction of an infinite class of new Sasaki-Einstein manifolds in dimension 2k + 3 given a positive curvature Kähler-Einstein base manifold in dimension 2k. For k = 1 these describe new supergravity duals for N = 1 superconformal field theories with both rational and irrational R-charges and central charge. We also present a generalization of this construction, that has not appeared elsewhere in the literature, to the case where the base is a product of Kähler-Einstein manifolds.
Supersymmetric AdS 5 solutions of M-theory
Classical and Quantum Gravity, 2004
We analyse the most general supersymmetric solutions of D = 11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M 6 , with four-form flux on M 6 . We show that M 6 is partly specified by a one-parameter family of four-dimensional Kähler metrics. We find a large family of new explicit regular solutions where M 6 is a compact, complex manifold which is topologically a two-sphere bundle over a four-dimensional base, where the latter is either (i) Kähler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T 1,1 /Z 2 . Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.