Nakwoo Kim

Fivebranes Wrapped on SLAG Three-Cycles and Related Geometry

We construct ten-dimensional supergravity solutions corresponding to the near horizon limit of IIB fivebranes wrapping special lagrangian three-cycles of constant curvature. The case of branes wrapping a three-sphere provides a gravity dual of pure = 2 super--Yang-Mills theory in D = 3. The non-trivial part of the solutions are seven manifolds that admit two G2 structures each of which is covariantly constant with respect to a different connection with torsion. We derive a formula for the generalised calibration for this general class of solutions. We discuss analogous aspects of the geometry that arises when fivebranes wrap other supersymmetric cycles which lead to Spin(7) and SU(N) structures. In some cases there are two covariantly constant structures and in others one.

M-fivebranes wrapped on supersymmetric cycles

We construct supergravity solutions dual to the twisted field theories arising when M-theory fivebranes wrap general supersymmetric cycles. The solutions are constructed in maximal D=7 gauged supergravity and then uplifted to D=11. Our analysis covers Kaehler, special Lagrangian and exceptional calibrated cycles. The metrics on the cycles are Einstein, but do not necessarily have constant curvature. We find many new examples of AdS/CFT duality, corresponding to the IR superconformal fixed points of the twisted field theories.

Wrapped M5-branes, consistent truncations and AdS/CMT

At the level of the bosonic fields, we construct consistent Kaluza-Klein reductions of D = 11 supergravity on Σ3 × S4, where Σ3 = H3/Γ, S3/Γ or R3/Γ where Γ is a discrete group of isometries. The result is the bosonic content of an N = 2 D = 4 gauged supergravity with a single vector multiplet and two hypermultiplets, whose scalar fields parametrise SU(1,1)/U(1) × G2(2)/SO(4). When Σ3 = H3/Γ the D = 4 theory has an AdS4 vacuum which uplifts to the known supersymmetric AdS4 × H3/Γ × S4 solution of D = 11 supergravity that describes the N = 2 d = 3 SCFT arising when M5-branes wrap SLag 3-cycles H3/Γ in Calabi-Yau three-folds. We use the KK reduction for Σ3 = H3/Γ to construct D = 11 black hole solutions that describe these d = 3 SCFTs at finite temperature and charge density and show that there is a superconducting instability involving a charged scalar field, and another instability involving neutral fields including both scalar and vector fields. We also use this KK reduction to construct a D = 11 Lifshitz solution that is dual to a d = 3 field theory with dynamical exponent z ∼ 39.

Five-branes wrapped on associative three cycles

We construct supergravity solutions corresponding to fivebranes wrapping associative three-cycles of constant curvature in manifolds of

Wrapped five-branes and N=2 superYang-Mills theory

{G}_{2}

Plane-wave Matrix Theory from N=4 Super Yang-Mills on RxS3

-holonomy. The solutions preserve 2 supercharges and are first constructed in

On the Spectrum of PP-Wave Matrix Theory

D=7

Superstring on pp-wave orbifold from large-N quiver gauge theory

gauged supergravity and then lifted to

AdS3 solutions of IIB supergravity from D3-branes

D=10,11.

Membranes wrapped on holomorphic curves

We show that the low-energy theory of M-fivebranes wrapped on a compact hyperbolic three-space is dual to a superconformal field theory in