3D superconformal theories from Sasakian seven-manifolds: new non-trivial evidences for

Abstract

In this paper we discuss candidate superconformal N = 2 gauge theories that realize the AdS/CFT correspondence with M-theory compactified on the homogeneous Sasakian 7-manifolds M 7 that were classified long ago. In particular we focus on the two cases M 7 = Q 1,1,1 and M 7 = M 1,1,1 , for the latter the Kaluza Klein spectrum being completely known. We show how the toric description of M 7 suggests the gauge group and the supersingleton fields. The conformal dimensions of the latter can be independently calculated by comparison with the mass of baryonic operators that correspond to 5-branes wrapped on supersymmetric 5-cycles and are charged with respect to the Betti multiplets. The entire Kaluza Klein spectrum of short multiplets agrees with these dimensions. Furthermore, the metric cone over the Sasakian manifold is a conifold algebraically embedded in some C p . The ring of chiral primary fields is defined as the coordinate ring of C p modded by the ideal generated by the embedding equations; this ideal has a nice characterization by means of representation theory. The entire Kaluza Klein spectrum is explained in terms of these vanishing relations. We give the superfield interpretation of all short multiplets and we point out the existence of many long multiplets with rational protected dimensions, whose presence and pattern were already noticed in other compactifications and seem to be universal. * Supported in part by EEC under TMR contract ERBFMRX-CT96-0045 and by GNFM.

More on Penrose limit of AdS4×Q1,1,1

“…The base is parametrized by the spherical coordinates (θ i , φ i ), i = 1, 2, 3 to parametrize i-th two sphere, as usual, and the angle ψ which has period 4π parametrizes the U(1) Hopf fiber. The SU(2) 1 × SU(2) 2 × SU(2) 3 × U(1) R isometry group of Q 1,1,1 corresponds to SU(2) 1 × SU(2) 2 × SU(2) 3 global symmetry and U(1) R R-symmetry of the dual superconformal field theory of [45]. Let us make a scaling limit around a null geodesic in AdS 4 × Q 1,1,1 that rotates along the ψ coordinate of Q 1,1,1 whose shift symmetry corresponds to the U(1) R symmetry in the dual superconformal field theory.…”

“…3 Gauge Theory Spectrum color representation [45]. At the fixed point, these chiral superfields have conformal weight 1/3 and transform as (2, 1, 1), (1, 2, 1) and…”

“…Moreover R charge is 0. So this corresponds to the massless graviton multiplet that propagates in the AdS 4 bulk [45].…”

“…This corresponds to the massless vector multiplet propagating in the AdS 4 bulk [45]. There are also two massless vector multiplets denoted by (1, 3, 1) 0 and (1, 1, 3) 0 coming from the permutation of three SU(2) flavor groups.…”

“…It was shown in [45] that from the harmonic analysis on Q 1,1,1 and the spectrum of SU(2) 1 × SU(2) 2 × SU(2) 3 representation of the OSp(2|4) hypermultiplets, the hypermultiplet of conformal dimension ∆ = R and U(1) charge s = R/2 should be in the representation l i = s = R/2.…”