In this talk we will consider the spectrum of anomalous dimensions in N=4 super-Yang-Mills and related theories. We will first discuss the emergence of quantum chaos as one goes from infinite to finite N and how the perturbative spectrum is described by GOE random matrix theory. We will then describe how the integrability of the planar-limit can be used to rewrite the computation of the leading 1/N corrections to the one-loop anomalous dimensions in terms of scalar products of off-shell Bethe states or, alternatively, hexagon-like functions.---- Part of London Integrability Journal Club. If you are a new participant, please register filling the form at integrability-london.weebly.com. The link will be emailed.

Higher-spin fields can play an important role in effective field theories and increasingly are of interest due to their appearance in recent studies of holography. Understanding their interactions is however often involved and searching for alternative formulations could be very useful. In this talk we will consider one such formulation, namely twistors. After giving a general introduction to the use of twistors in describing the dynamics of massless field theories, we will focus on the construction of off-shell actions directly in twistor space including a recent higher-spin generalisation of self-dual Weyl gravity. We will show how this formulation produces the expected flat space-time spectrum and linearised symmetries. In analogy with the known embedding of Einstein gravity inside Weyl gravity, we identify a ghost free sub-sector of the conformal higher-spin theory and consider its cubic couplings. Finally we describe proposed anti-self-dual interaction terms to extend the twistor action to the full conformal higher-spin theory.

In this talk we will briefly review the recent progress in the semiclassical string theory calculation of non-BPS gauge theory three-point correlation functions at strong coupling. We will then discuss the light-cone path integral approach to such three-point functions with a focus on near-BMN operators where one can systematically go beyond the semiclassical approximation.

There has been much recent interest in the proposed duality between superstrings in the curved geometry AdS_4 x P3 and three dimensional N=6 supersymmetric Chern-Simons theory -- a new, concrete, example of the holographic AdS/CFT correspondence. This dual pair has additionally been conjectured to be an integrable system in the planar limit. In this talk I will discuss several classes of classical strings moving in this background, and their quantum corrections, as tools to probe the duality and to test the conjectured integrable structure.