SCFT and M theory on AdS4×Q1,1,1

2010

We study U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau four-fold singularities. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying non-zero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing six-cycles, and study in detail the cone over Q^{111}. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gauge-invariant baryonic-type operators in this theory and wrapped M5 brane states. Moreover, the physics of vacua in which these symmetries are spontaneously broken precisely matches a dual gravity analysis involving resolutions of the singularity, where we are able to match condensates of the baryonic operators, Goldstone bosons and global strings. We also argue more generally that theories where the resolutions have six-cycles are expected to receive non-perturbative corrections from M5 brane instantons. We give a general formula relating the instanton action to normalizable harmonic two-forms, and compute it explicitly for the Q^{222} example. The holographic interpretation of such instantons is currently unclear.

Journal of High Energy Physics, 1998

I identify a correspondence between the various spherical harmonic modes of massless 11 dimensional fields propagating on the AdS 4/7 in an AdS 4/7 × S 7/4 compactification of M theory, and the corresponding operators, primary under the conformal group, on the world volume of the M 2 , M 5 branes. This is achieved by matching representations of the superconformal algebra on the two sides of the correspondence.

Nuclear Physics B, 2000

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 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 seem to be universal in all compactifications. * Supported in part by EEC under TMR contract ERBFMRX-CT96-0045 and by GNFM.

Journal of High Energy Physics, 2009

We construct three-dimensional N = 2 Chern-Simons-quiver theories which are holographically dual to the M-theory Freund-Rubin solutions AdS 4 × V 5,2 /Z k (with or without torsion G-flux), where V 5,2 is a homogeneous Sasaki-Einstein seven-manifold. The global symmetry group of these theories is generically SU (2) × U (1) × U (1) R , and they are hence non-toric. The field theories may be thought of as the n = 2 member of a family of models, labelled by a positive integer n, arising on multiple M2-branes at certain hypersurface singularities. We describe how these models can be engineered via generalized Hanany-Witten brane constructions. The AdS 4 × V 5,2 /Z k solutions may be deformed to a warped geometry R 1,2 ×T * S 4 /Z k , with self-dual G-flux through the four-sphere. We show that this solution is dual to a supersymmetric mass deformation, which precisely modifies the classical moduli space of the field theory to the deformed geometry.

Physics Letters B, 1998

We consider D3 branes world-volume theories substaining N = 1, 2 superconformal field theories. Under the assumption that these theories are dual to N = 2, 4 supergravities in AdS 5 , we explore the general structure of the latter and discuss some issues when comparing the bulk theory to the boundary singleton theory.

2012

We engineer a large new set of four-dimensional N = 1 superconformal field theories by wrapping M5-branes on complex curves. We present new supersymmetric AdS 5 M-theory backgrounds which describe these fixed points at large N , and then directly construct the dual four-dimensional CFTs for a certain subset of these solutions. Additionally, we provide a direct check of the central charges of these theories by using the M5-brane anomaly polynomial. This is a companion paper which elaborates upon results reported in [1].

Journal of High Energy Physics

We consider N=4 SU(2)xU(1) gauged supergravity on asymptotically-AdS_5 backgrounds. By a near-boundary analysis we determine the boundary-dominant components of the bulk fields from their partially gauge-fixed field equations. Subdominant components are projected out in the boundary limit and we find a reduced set of boundary fields, constituting the N=2 Weyl multiplet. The residual bulk symmetries are found to act on the boundary fields as four-dimensional diffeomorphisms, N=2 supersymmetry and (super-)Weyl transformations. This shows that the on-shell N=4 supergravity multiplet yields the N=2 Weyl multiplet on the boundary with the appropriate local N=2 superconformal transformations. Building on these results we use the AdS/CFT conjecture to calculate the Weyl anomaly of the dual four-dimensional superconformal field theories in a generic bosonic N=2 conformal supergravity background.

It is argued that N=6 supergravity on AdS 5 , with gauge group SU(3) × U(1) corresponds, at the classical level, to a subsector of the "chiral" primary operators of N=4 Yang-Mills theories. This projection involves a "duality transformation" of N=4 Yang-Mills theory and therefore can be valid if the coupling is at a self-dual point, or for those amplitudes that do not depend on the coupling constant.

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.

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.