Singularity Resolution in Gauged Supergravity and Conifold Unification

We obtain a unified picture for the conifold singularity resolution. We propose that gauged supergravity, through a novel prescription for the twisting, provides an appropriate framework to smooth out singularities in the context of gravity duals of supersymmetric gauge theories.Comment: 13 pages, harvmac, one figure; v2: reference adde

Let's Twist Again: General Metrics of G(2) Holonomy from Gauged Supergravity

We construct all complete metrics of cohomogeneity one G(2) holonomy with S^3 x S^3 principal orbits from gauged supergravity. Our approach rests on a generalization of the twisting procedure used in this framework. It corresponds to a non-trivial embedding of the special Lagrangian three-cycle wrapped by the D6-branes in the lower dimensional supergravity. There are constraints that neatly reduce the general ansatz to a six functions one. Within this approach, the Hitchin system and the flop transformation are nicely realized in eight dimensional gauged supergravity.Comment: 31 pages, latex; v2: minor changes, references adde

Prepotential and Instanton Corrections in N=2 Supersymmetric SU(N_1)xSU(N_2) Yang Mills Theories

In this paper we analyse the non-hyperelliptic Seiberg-Witten curves derived from M-theory that encode the low energy solution of N=2 supersymmetric theories with product gauge groups. We consider the case of a SU(N_1)xSU(N_2) gauge theory with a hypermultiplet in the bifundamental representation together with matter in the fundamental representations of SU(N_1) and SU(N_2). By means of the Riemann bilinear relations that hold on the Riemann surface defined by the Seiberg--Witten curve, we compute the logarithmic derivative of the prepotential with respect to the quantum scales of both gauge groups. As an application we develop a method to compute recursively the instanton corrections to the prepotential in a straightforward way. We present explicit formulas for up to third order on both quantum scales. Furthermore, we extend those results to SU(N) gauge theories with a matter hypermultiplet in the symmetric and antisymmetric representation. We also present some non-trivial checks of our results.Comment: 21 pages, 2 figures, minor changes and references adde

Wrapped branes with fluxes in 8d gauged supergravity

We study the gravity dual of several wrapped D-brane configurations in presence of 4-form RR fluxes partially piercing the unwrapped directions. We present a systematic approach to obtain these solutions from those without fluxes. We use D=8 gauged supergravity as a starting point to build up these solutions. The configurations include (smeared) M2-branes at the tip of a G_2 cone on S^3 x S^3, D2-D6 branes with the latter wrapping a special Lagrangian 3-cycle of the complex deformed conifold and an holomorphic sphere in its cotangent bundle T^*S^2, D3-branes at the tip of the generalized resolved conifold, and others obtained by means of T duality and KK reduction. We elaborate on the corresponding N=1 and N=2 field theories in 2+1 dimensions.Comment: 32 pages, LateX, v2: minor changes, reference added, v3: section 3.5.2 improve

Chern-Simons Vortices in Supergravity

We study supersymmetric vortex solutions in three-dimensional abelian gauged supergravity. First, we construct the general U(1)-gauged D=3, N=2 supergravity whose scalar sector is an arbitrary Kahler manifold with U(1) isometry. This construction clarifies the connection between local supersymmetry and the specific forms of some scalar potentials previously found in the literature -- in particular, it provides the locally supersymmetric embedding of the abelian Chern-Simons Higgs model. We show that the Killing spinor equations admit rotationally symmetric vortex solutions with asymptotically conical geometry which preserve half of the supersymmetry.Comment: 26 pages, LaTeX2

Multi-Instanton Calculus and Equivariant Cohomology

We present a systematic derivation of multi-instanton amplitudes in terms of ADHM equivariant cohomology. The results rely on a supersymmetric formulation of the localization formula for equivariant forms. We examine the cases of N=4 and N=2 gauge theories with adjoint and fundamental matter.Comment: 29 pages, one more reference adde

Mirror Symmetry and a G2G_2 Flop

By applying mirror symmetry to D-branes in a Calabi-Yau geometry we shed light on a $G_2$ flop in M-theory relevant for large $N$ dualities in ${\cal N}=1$ supersymmetric gauge theories. Furthermore, we derive superpotential for M-theory on corresponding $G_2$ manifolds for all A-D-E cases. This provides an effective method for geometric engineering of ${\cal N}=1$ gauge theories for which mirror symmetry gives exact information about vacuum geometry. We also find a number of interesting dual descriptions.Comment: Identification of parameters as well as the computation of the superpotential is extended to all A-D-E cases. Additional references are also include

Branes with fluxes wrapped on spheres

Following an eight-dimensional gauged supergravity approach we construct the most general solution describing D6-branes wrapped on a Kahler four-cycle taken to be the product of two spheres of different radii. Our solution interpolates between a Calabi-Yau four-fold and the spaces S^2xS^2xS^2xR^2 or S^2xS^2xR^4, depending on generic choices for the parameters. Then we turn on a background four-form field strength, corresponding to D2-branes, and show explicitly how our solution is deformed. For a particular choice of parameters it represents a flow from a Calabi-Yau four-fold times the three-dimensional Minkowski space-time in the ultraviolet, to the space-time AdS_4xQ^{1,1,1} in the infrared. In general, the solution in the infrared has a singularity which within type-IIA supergravity corresponds to the near horizon geometry of the solution for the D2-D6 system. Finally, we uncover the relation with work done in the eighties on Freund-Rubin type compactifications.Comment: 15 pages, Late

Hydrodynamics from the Dp-brane

We complete the computation of viscous transport coefficients in the near horizon geometries that arise from a stack of black Dp-branes for p=2,...,6 in the decoupling limit. The main new result is the obtention of the bulk viscosity which, for all p, is found to be related to the speed of sound by the simple relation \zeta/\eta = -2(v_s^2-1/p). For completeness the shear viscosity is rederived from gravitational perturbations in the shear and scalar channels. We comment on technical issues like the counterterms needed, or the possible dependence on the conformal frame.Comment: 15 page

BPS String Solutions in Non-Abelian Yang-Mills Theories and Confinement

Starting from the bosonic part of N=2 Super QCD with a 'Seiberg-Witten' N=2 breaking mass term, we obtain string BPS conditions for arbitrary semi-simple gauge groups. We show that the vacuum structure is compatible with a symmetry breaking scheme which allows the existence of Z_k-strings and which has Spin(10) -> SU(5) x Z_2 as a particular case. We obtain BPS Z_k-string solutions and show that they satisfy the same first order differential equations as the BPS string for the U(1) case. We also show that the string tension is constant, which may cause a confining potential between monopoles increasing linearly with their distance.Comment: 11 pages, Latex. Minor changes to the text. Final version to appear in Phys. Rev.