Exact solution of 4d nonlinear bosonic higher-spin gauge theory, that provides a higher-spin deformation of the AdS4 Schwarzschild black hole, is found.

TBA

The N=2 boundary superspace formulation of RNS models in the presence of arbitrary NSNS fluxes is developed. This allows for a systematic classification of supersymmetric D-brane configuration which leads e.g. to generalized lagrangian and coisotropic branes.

Recent work on membranes of M-theory has lead to a new type of physical realization of fuzzy 2-spheres in Matrix Brane actions. In standard realizations, the fuzzy two-sphere coordinates transforming in the vector of the spherical rotation symmetry are identified with matrix variables in the adjoint representation of the unitary symmetry of the Matrix brane actions.In these new realizations, spinors of the rotational symmetry are identified with variables in bi-fundamental representations of the unitary symmetry. The vector coordinates of the fuzzy 2-sphere are recovered from bilinears in the spinors by a fuzzy version of the projection map of the Hopf fibration over the two-sphere. The outcome is the emergence of a five dimensional theory from a three dimensional one as expected from the intersection of the fundamental branes of M-Theory in ABJM quotients of eleven dimensional spacetime. The demonstration of the emergent six dimensional theory expected for the brane intersection in M-Theory without a quotient remains an open problem.

In the first part of the talk I will review differential geometric background involving associative submanifolds of 7 manifolds with G2 holonomy and an analogue of the Yang Mills instanton equation for connections on bundles over such a manifold. Then I will describe joint work with Ed Segal in which, assuming these objects have suitable formal properties, we define holomorphic bundles over moduli spaces of Calabi-Yau 3-folds which can be viewed as the complexification of Floer theory. In the last part of the talk I will consider in more detail the problem of establishing the foundations required for the theory. This involves pertubations of the equations and the question of how to count solutions at infinity, which are pairs consisting of a connection and an associative submanifold. The counting problem leads to a nonlinear generalisation of the spectral flow for eigenvalues of Dirac operators.

In this talk, we will review recent work which asks the question, what, if any effects stringy modifications to geometry might have on the predictions of inflation? We couch our discussion within two well motivated frameworks-- non-commutative geometry (likely to be present during brane inflation), and modifications to mode propagation coming from a field theory representation of the stringy uncertainty principle. In the former case, we find that UV/IR mode mixing can imprint potentially observable signatures onto the CMB independent of the scale of inflation. In the latter case, we analytically compute corrections, and comment on the possibility of observing these in the fortunate circumstance that we happen to find ourselves in a weakly coupled corner of moduli space.

We discuss quasi-classical quantization of AdS4 x CP3 superstring using the algebraic curve techinque. We exemplify this procedure on some configurations so called giant magnons. It turns out that there are two types of configurations and they are quantizied in slightly different ways. Also we discuss testing AdS/CFT correspondence in this case.

I will explain two algorithms that compute numerically the Weil-Petersson metric on the moduli space of polarized Calabi-Yau manifolds. I will show some explicit examples. Finally, I will outline some applications of these techniques in the physics of Calabi-Yau compactifications of string theory.

We introduce the Wilson loop/amplitude duality, which states that certain gluon amplitudes in N=4 SYM are equivalent to light-like polygonal Wilson loops. We will illustrate the duality's power by computing the one loop Wilson loop analytically (matching with the known amplitudes) and then the two loop Wilson loop numerically for any number of edges. If the duality continues to hold we can thus compute two loop MHV amplitudes for any number of incoming particles. In the second part of the talk we discuss the recently conjectured new symmetry dual superconformal symmetry of the complete S-matrix of N=4 SYM. We prove its presence at tree-level and find new constraints it puts on the one loop amplitude.

In this talk, I will present several results concerning a class of supersymmetric Wilson loop operators in N=4 SYM. These operators can be defined for any loop on a three-sphere and are in general 1/16-BPS. On the string theory side of the AdS/CFT duality, these supersymmetric Wilson loops are described by string worldsheets which are pseudo-holomorphic with respect to a novel almost complex structure defined on a AdS4xS2 subspace of AdS5xS5. A notable subclass of the general 1/16-BPS operators, which will be the main focus of this talk, is obtained by restricting the loop to lie on a S2 in space-time. In this case supersymmetry is doubled, and we propose a conjecture that the expectation value of these operators can be computed exactly in terms of the analogous observables in bosonic 2d Yang-Mills on S2, or equivalently by a gaussian matrix model. Several evidences for this conjecture, both on the gauge theory and on the string theory side, will be presented.

We review a duality between N=4 super Yang-Mills and a string theory in AdS5xS5 background and integrability arising in both theories. New results conserning finite length operators/short strings will be presented.

We first quickly review some basic facts about quantum theories in 1+5 dimensions with 2,0 superconformal symmetry. They arise as decoupled subsectors of string or M theories on space times containing certain defects like branes or singularities. By compactification, they are also related to Yang-Mills theories in lower dimensions. We then describe, in somewhat more detail, recent work on these theories considered on a spatial five torus. In particular, one may determine the spectrum of vacuum states, and also learn much about the spectrum of BPS states. Hopefully, this will eventually be helpful for giving a definition of these mysterious theories.

We attempt to indirectly deduce the form of quantum geometry on the M5-brane in the presence of a constant C-field 3-form potential. We first show how the noncommutative geometry on the D3-brane in a constant 2-form B-field can be deduced by analysing open strings ending on the D3-brane. We show that the string boundary condition is a modified Nahm equation, and that these modifications can be understood in terms of the noncommutative geometry. Similarly, the boundary condition for M2-branes ending on the M5-brane is given by the Basu-Harvey equation, modified by the C-field. By an analogy, we interpret this modification in terms of a proposed quantum geometry on the M5-brane. This geometry is specified by a 3-bracket, unlike the usual 2-bracket for noncommutative geometry.

In some recent work with Kronheimer we have carried over a version of Juhasz' Heegaard Floer Homology for sutured three manifolds to Instanton Floer Homology. This leads to amongst over things a streamlined proofs of property P for all knots and that symplectic manifolds have non-vanishing Donaldson invariants.

From dimer models, as introduced in string theory, we can produce a class of Calabi Yau algebras which are candidates for non-commutative crepant resolutions of Gorenstein 3 fold affine toric singularities. In this talk I will introduce, via examples, dimers and their corresponding toric varieties. I will then talk about the consistency condition that underlies the Calabi Yau property.

The AdS4/Chern-Simons theory duality, recently conjectured by Aharony, Bergman, Jafferis and Maldacena, provides not only a new testing ground for the gauge theory/gravity correspondence, but also a possible way to access M-theoretic degrees of freedom. In this talk, I shall discuss some of our recent results on the open string sector of the type IIA string theory in AdS4xCP3, with emphasis on D-branes and giant gravitons in particular. Specifically, I shall focus on the so-called dual giant, a D2-brane extended on an S2 in AdS4, its spectrum of small fluctuations and open strings attached to it.