Gravity duals of supersymmetric gauge theories on three-manifolds

We study gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector, finding a simple closed formula when the solution has U(1) x U(1) symmetry. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localization. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories with a large N limit, defined on a general class of background three-manifold geometries.Comment: 74 pages, 2 figures; v2: minor change

A dual view of the 3d Heisenberg model and the abelian projection

The Heisenberg model in 3d is studied from a dual point of view. It is shown that it can have vortex configurations, carrying a conserved charge(U(1) symmetry). Vortices condens in the disordered phase. A disorder parameter \leftangle\mu\rightangle is defined dual to the magnetization \leftangle\vec n\rightangle, which signals condensation of vortices, i.e. spontaneous breaking of the dual U(1) symmetry. This study sheds light on the procedure known as abelian projection in non abelian gauge theories.Comment: LateX, 15 pages, 3 figure

Pool temperature stratification analysis in CIRCE-ICE facility with RELAP5-3D© model and comparison with experimental tests

In the frame of heavy liquid metal (HLM) technology development, CIRCE pool facility at ENEA/Brasimone Research Center was updated by installing ICE (Integral Circulation Experiments) test section which simulates the thermal behavior of a primary system in a HLM cooled pool reactor. The experimental campaign led to the characterization of mixed convection and thermal stratification in a HLM pool in safety relevant conditions and to the distribution of experimental data for the validation of CFD and system codes. For this purpose, several thermocouples were installed into the pool using 4 vertical supports in different circumferential position for a total of 119 thermocouples [1][2]. The aim of this work is to investigate the capability of the system code RELAP5-3D (c) to simulate mixed convection and thermal stratification phenomena in a HLM pool in steady state conditions by comparing code results with experimental data. The pool has been simulated by a 3D component divided into 1728 volumes, 119 of which are centered in the exact position of the thermocouples. Three dimensional model of the pool is completed with a mono-dimensional nodalization of the primary main flow path. The results obtained by code simulations are compared with a steady state condition carried out in the experimental campaign. Results of axial, radial and azimuthal temperature profile into the pool are in agreement with the available experimental data Furthermore the code is able to well simulate operating conditions into the main flow path of the test section

Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields

The localization formula of Chern-Simons quiver gauge theory on $S^3$ nicely reproduces the geometric data such as volume of Sasaki-Einstein manifolds in the large-$N$ limit, at least for vector-like models. The validity of chiral-like models is not established yet, due to technical problems in both analytic and numerical approaches. Recently Gulotta, Herzog and Pufu suggested that the counting of chiral operators can be used to find the eigenvalue distribution of quiver matrix models. In this paper we apply this method to some vector-like or chiral-like quiver theories, including the triangular quivers with generic Chern-Simons levels which are dual to in-homogeneous Sasaki-Einstein manifolds $Y^{p,k}(\mathbb{CP}^2)$. The result is consistent with AdS/CFT and the volume formula. We discuss the implication of our analysis.Comment: 23 pages; v2. revised version; v3. corrected typos and clarified argument

Semiclassical strings in marginally deformed toric AdS/CFT

We study string solutions in the beta-deformed Sasaki-Einstein gauge/gravity dualities. We find that the BPS point-like strings move in the submanifolds where the two U(1) circles shrink to zero size. In the corresponding T^3 fibration description, the strings live on the edges of the polyhedron, where the T^3 fibration degenerates to T^1. Moreover, we find that for each deformed Sasaki-Einstein manifold the BPS string solutions exist only for particular values of the deformation parameter. Our results imply that in the dual field theory the corresponding BPS operators exist only for these particular values of the deformation parameter we find. We also examine the non-BPS strings, derive their dispersion relations and compare them with the undeformed ones. Finally, we comment on the range of the validity of our solutions and their dependence on the deformation parameter.Comment: 29 pages, 9 figure

Uniqueness and examples of compact toric Sasaki-Einstein metrics

In [11] it was proved that, given a compact toric Sasaki manifold of positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed Sasaki structure on which a Sasaki-Einstein metric exists. In the present paper we first prove the uniqueness of such Einstein metrics on compact toric Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure, and secondly remark that the result of [11] implies the existence of compatible Einstein metrics on all compact Sasaki manifolds obtained from the toric diagrams with any height, or equivalently on all compact toric Sasaki manifolds whose cones have flat canonical bundle. We further show that there exists an infinite family of inequivalent toric Sasaki-Einstein metrics on $S^5 \sharp k(S^2 \times S^3)$ for each positive integer $k$.Comment: Statements of the results are modifie

M-theory and Seven-Dimensional Inhomogeneous Sasaki-Einstein Manifolds

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 $KE_4=\mathbb{CP}^2$ base are proposed only within a restricted range $3p/2\le k \le 2p$ as ${\cal N}=2$ quiver Chern-Simons-matter theories with $SU(N)\times SU(N)\times SU(N)$ 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 ${\rm AdS}_4\times Y^{p,k}$, and are dual to protected operators written in terms of matter multiplets in the dual conformal field theory.Comment: v2 refs added. 19 pages 1 figur