AdS/CFT Correspondence and Type 0 String Theory

We review some applications of Type 0 string theory in the context of the AdS/CFT correspondence.Comment: 6 pages, LaTeX + JHEP.cls, talk presented at the TMR conference ``Quantum aspects of gauge theories, supersymmetry and unification'', Paris, September 1-7, 199

The gravity dual of supersymmetric gauge theories on a squashed S1×S3S^1 \times S^3

We present a new one-parameter family of supersymmetric solutions deforming AdS_5. This is constructed as an asymptotically locally anti de Sitter (AlAdS) solution of five-dimensional minimal gauged supergravity, with topology R x R^4 and a non-trivial graviphoton field, and can be uplifted to ten or eleven dimensional supergravities. An analytic continuation of this solution yields the gravity dual to a class of four-dimensional N=1 supersymmetric gauge theories on a curved manifold with topology S^1 x S^3, comprising an SU(2) x U(1)-symmetric squashed three-sphere, with a non-trivial background gauge field coupling to the R-symmetry current. We compute the holographically renormalised on-shell action and interpret it in terms of the Casimir energy of the dual field theory. We also determine the holographic conserved charges of the solution and discuss relations between them.Comment: 57 pages, 5 figures. v4: version published in JHE

Baryonic branches and resolutions of Ricci-flat Kahler cones

We consider deformations of N=1 superconformal field theories that are AdS/CFT dual to Type IIB string theory on Sasaki-Einstein manifolds, characterised by non-zero vacuum expectation values for certain baryonic operators. Such baryonic branches are constructed from (partially) resolved, asymptotically conical Ricci-flat Kahler manifolds, together with a choice of point where the stack of D3-branes is placed. The complete solution then describes a renormalisation group flow between two AdS fixed points. We discuss the use of probe Euclidean D3-branes in these backgrounds as a means to compute expectation values of baryonic operators. The Y^{p,q} theories are used as illustrative examples throughout the paper. In particular, we present supergravity solutions describing flows from the Y^{p,q} theories to various different orbifold field theories in the infra-red, and successfully match this to an explicit field theory analysis.Comment: 51 pages, v2: reference added and minor changes; v3: minor changes, published versio

Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals

Recently an infinite family of explicit Sasaki-Einstein metrics Y^{p,q} on S^2 x 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 Kahler 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}xZ_{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.Comment: 54 pages, 5 figures; minor changes; further minor changes, ref [8] added - published version; eqns 1.3, 1.4 remove

Symmetry-breaking vacua and baryon condensates in AdS/CFT

We study the gravity duals of symmetry-breaking deformations of superconformal field theories, AdS/CFT dual to Type IIB string theory on AdS_5 x Y where Y is a Sasaki-Einstein manifold. In these vacua both conformal invariance and baryonic symmetries are spontaneously broken. We present a detailed discussion of the supergravity moduli space, which involves flat form fields on asymptotically conical Calabi-Yau manifolds, and match this to the gauge theory vacuum moduli space. We discuss certain linearised fluctuations of the moduli, identifying the Goldstone bosons associated with spontaneous breaking of non-anomalous baryonic symmetries. The remaining moduli fields are related to spontaneous breaking of anomalous baryonic symmetries. We also elaborate on the proposal that computing condensates of baryon operators is equivalent to computing the partition function of a non-compact Euclidean D3-brane in the background supergravity solution, with fixed boundary conditions at infinity.Comment: 121 pages; v2: references adde

The large N limit of quiver matrix models and Sasaki-Einstein manifolds

We study the matrix models that result from localization of the partition functions of N=2 Chern-Simons-matter theories on the three-sphere. A large class of such theories are conjectured to be holographically dual to M-theory on Sasaki-Einstein seven-manifolds. We study the M-theory limit (large N and fixed Chern-Simons levels) of these matrix models for various examples, and show that in this limit the free energy reproduces the expected AdS/CFT result of N^{3/2}/Vol(Y)^{1/2}, where Vol(Y) is the volume of the corresponding Sasaki-Einstein metric. More generally we conjecture a relation between the large N limit of the partition function, interpreted as a function of trial R-charges, and the volumes of Sasakian metrics on links of Calabi-Yau four-fold singularities. We verify this conjecture for a family of U(N)^2 Chern-Simons quivers based on M2 branes at hypersurface singularities, and for a U(N)^3 theory based on M2 branes at a toric singularity.Comment: 38 pages, 4 figures; v2: minor changes, typos and factor of 2 in eq. (5.19) fixed, references and 2 figures added; v3: new section 4.5 added; v4: more typos fixed, range of validity of (4.19) clarifie

The gravity dual of supersymmetric gauge theories on a two-parameter deformed three-sphere

We present rigid supersymmetric backgrounds for three-dimensional N=2 supersymmetric gauge theories, comprising a two-parameter U(1)xU(1)-invariant deformed three-sphere, and their gravity duals. These are described by supersymmetric solutions of four-dimensional N=2 gauged supergravity with a self-dual metric on the ball and different instantons for the graviphoton field. We find two types of solutions, distinguished by their holographic free energies. In one type the holographic free energy is constant, whereas in another type it depends in a simple way on the parameters and is generically complex. This leads to a conjecture for the localized partition function of a class of N=2 supersymmetric gauge theories on these backgrounds.Comment: 27 pages, 1 figure; v2: typos fixed, minor changes, one reference adde