http://inspirehep.net/record/499969/files/arXiv:hep-th_9905111.pdf

Large N Field Theories, String Theory and Gravity

We construct three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(N) and SU(N) × SU(N) which have explicit = 6 superconformal symmetry. Using brane constructions we argue that the U(N) × U(N) theory at level k describes the low energy limit of N M2-branes probing a C4/Zk singularity. At large N the theory is then dual to M-theory on AdS4 × S7/Zk. The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS4 × CP3. For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU(2) × SU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.

N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals

http://inspirehep.net/record/393570/files/arXiv:hep-th_9503124.pdf

String theory dynamics in various dimensions

Unity of superstring dualities

Superstring theoryをめぐって(放談室)

All purely bosonic supersymmetric solutions of minimal supergravity in five dimensions are classified. The solutions preserve either one half or all of the supersymmetry. Explicit examples of new solutions are given, including a large family of plane-fronted waves and a maximally supersymmetric analogue of the Godel universe which lifts to a solution of 11-dimensional supergravity that preserves 20 supersymmetries.

All supersymmetric solutions of minimal supergravity in five- dimensions

We present a countably infinite number of new explicit co-homogeneity one Sasaki-Einstein metrics on $S^2\times S^3$ of both quasi-regular and irregular type. These give rise to new solutions of type IIB supergravity which are expected to be dual to $\mathcal{N}=1$ superconformal field theories in four dimensions with compact or non-compact $R$-symmetry and rational or irrational central charges, respectively.

/pdf/sasaki-einstein-metrics-on-s-2-x-s-3-59tlr4k2um.pdf

Sasaki-Einstein Metrics on S^2 x S^3

We analyze the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form ${R}^{1,9\ensuremath{-}d}\ifmmode\times\else\texttimes\fi{}{M}_{d},$ in the common Neveu-Schwarz--Neveu-Schwarz (NS-NS) sector of type II string theory and also type I or heterotic string theory. The results are phrased in terms of the intrinsic torsion of G structures and provide a comprehensive classification of static supersymmetric backgrounds in these theories. Generalized calibrations naturally appear since the geometries can always arise as solutions describing NS or type I or heterotic fivebranes wrapping calibrated cycles. Some new solutions are presented. In particular we find $d=6$ examples with a fibered structure which preserve $\mathcal{N}=1,2,3$ supersymmetry in type II and include compact type I or heterotic geometries.

Superstrings with intrinsic torsion

We propose a way to classify the local form of all bosonic supersymmetric configurations of D = 11 supergravity, using the differential forms that can be constructed as bi-linears from the Killing spinors. We show that the most general bosonic geometries either have a privileged SU(5) or a (Spin(7)8) × structure, depending on whether the Killing vector constructed from the Killing spinor is timelike or null, respectively. In the time-like case we derive the general local form of the geometry and show that it is almost completely determined by a certain SU(5) structure on the ten-dimensional space orthogonal to the orbits of the Killing vector. We also deduce what further conditions must be imposed in order that the equations of motion are satisfied. We illustrate the formalism with some known solutions and also present some new solutions including a rotating generalisation of the resolved membrane solutions and generalisations of the recently constructed D = 11 Godel solution. We also prove some general vanishing theorems for compactifications with flux.

The geometry of D = 11 Killing spinors

We analyse the geometrical structure of supersymmetric solutions of type II supergravity of the form Open image in new window1,9−n×Mn with non-trivial NS flux and dilaton. Solutions of this type arise naturally as the near-horizon limits of wrapped NS fivebrane geometries. We concentrate on the case d=7, preserving two or four supersymmetries, corresponding to branes wrapped on associative or SLAG three-cycles. Given the existence of Killing spinors, we show that M7 admits a G2-structure or an SU(3)-structure, respectively, of specific type. We also prove the converse result. We use the existence of these geometric structures as a new technique to derive some known and new explicit solutions, as well as a simple theorem implying that we have vanishing NS three-form and constant dilaton whenever M7 is compact with no boundary. The analysis extends simply to other type II examples and also to type I supergravity.

Jerome P. Gauntlett

Papers

All supersymmetric solutions of minimal supergravity in five- dimensions

Sasaki-Einstein Metrics on S^2 x S^3

Superstrings with intrinsic torsion

The geometry of D = 11 Killing spinors

G-Structures and Wrapped NS5-Branes