Week 22.02.2009 – 28.02.2009

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.

In this talk we will review the recent developments in the field of integrability of the AdS/CFT correspondence. In particular, we will discuss the novel dynamical tests of the duality and summarize the breakdown of the asymptotic spin-chain picture at the wrapping order. We will also discuss the latest attempts to incorporate the non-local wrapping interactions.

First we review existing results concerning the non-planar spectrum of N=4 SYM. Next, using an effective vertex method we explicitly derive the two-loop dilatation generator of ABJM theory in its SU(2) x SU(2) sector, including all non-planar corrections. This generator is then applied to a series of finite length operators as well as to two different types of BMN operators. As in N=4 SYM, at the planar level the finite length operators are found to exhibit a degeneracy between certain pairs of operators with opposite parity -- a degeneracy which can be attributed to the existence of an extra conserved charge and thus to the integrability of the planar theory.When non-planar corrections are taken into account the degeneracies between parity pairs disappear hinting the absence of higher conserved charges. The analysis of the BMN operators resembles that of N=4 SYM. Additional non-planar terms appear for BMN operators of finite length but once the strict BMN limit is taken these terms disappear.

In Landau-Ginzburg models, B-type boundary conditions are described by matrix factorisations of the superpotential. In cases where such a model corresponds to a rational conformal field theory (e.g. a coset model), we can compare the matrix factorisations to known boundary states. The connection between these complementary descriptions can on the one hand be used to improve the understanding of closed and open string moduli space, on the other hand it could give hints towards the construction of new boundary states.

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.