I will describe a new infinite set of AdS/CFT dual pairs which come from M5-branes wrapping Riemann surfaces. These solutions interpolate between and extend beyond a famous pair of solutions by Maldacena and Nunez. Additionally, the dual SCFTs are so-called "non-Lagrangian" theories, which have no weakly coupled UV description yet can (and will) be described explicitly.

The blackboard-talk will consist of an introductory part on two and three-point functions and their relation to the operator product expansion. In particular I will talk about "twist two operators" in N=4 SYM and other conformal theories and explain how you can calculate the structure constants of these three-point functions by only calculating two-point functions, and as a side effect also avoiding the need of information on the one-loop mixing matrix.

http://strings.ph.qmul.ac.uk/postgraduate/phd-courses

http://strings.ph.qmul.ac.uk/postgraduate/phd-courses

I will review the connection between the elliptic genus of K3 surfaces and the representation theory of the Mathieu group M_{24} and then discuss a proposed extension of this connection that applies to a larger set of groups and Jacobi forms.

The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. In this talk I will describe a new method to study these models in the M-theory limit, but at all orders in the 1/N expansion. The method is based on reformulating the matrix model as the partition function of a Fermi gas. This new approach leads to a completely elementary derivation of the N^{3/2} behavior for ABJM theory and other quiver Chern-Simons-matter theories. In addition, the full series of 1/N corrections to the original matrix integral can be simply determined by a next-to-leading calculation in the semiclassical expansion of the quantum gas.

In this talk I will discuss the elliptic genus of K3 (\phi_{K3}) both from a conformal field theory and an effective action point of view as an example of a BPS saturated quantity in string theory. In the former approach I will give evidence for an action of the Mathieu group M_{24} on the space of BPS states contributing to \phi_{K3} (Mathieu moonshine). On the effective action side I will present a new series of 1/4 BPS saturated one-loop amplitudes in type II string theory on K3xT^2 whose integrand can be related to derivatives of \phi_{K3}. I will evaluate explicitly a generating functional for this class of amplitudes and show that it is captured by the weight ten Igusa cusp form of Sp(4,Z). I conclude by speculating on possible algebraic implications of these results on the space of BPS states of the N=4 type II compactification.