Week 10.01.2010 – 16.01.2010

Freed-Witten anomaly is a global ambiguity of the string path integral measure in the presence of D-branes. It turns out it uniquely determines, by imposing its cancellation, the topological type of both the A and the B fields when restricted to the brane, as it naturally involves the interplay between open and closed string degrees of freedom. After introducing the suitable mathematical framework provided by the theory of gerbes with connections, I will try to characterize the nature of the gauge bundle on a brane in the most general closed string background. Furthermore, I will go over a case by case analysis, focusing on how it can account for fractional RR and Page charges and showing the physical relevance of the resulting K-theoretical improvement for classifying D-brane charges. Reference: L. Bonora, F. Ferrari Ruffino, R. S., arXiv: 0810.4291

Tremendous progress in computing perturbative scattering amplitudes in N=4 supersymmetric gauge theory has been made over the past few years. Importantly the planar amplitudes appear to display a dual conformal invariance next to the usual conformal symmetry. Altogether the symmetry enlarges to a Yangian algebra known from the context of integrable models. This infinite-dimensional symmetry might have the power to completely fix the S-matrix by algebraic means. In this talk we review the above developments. We then discuss conformal symmetry for tree and loop scattering amplitudes. It turns out that the free conformal symmetry generators are anomalous which calls for certain deformations to make the symmetries exact. These relate amplitude with different numbers of legs, and thus they contribute substantially to a complete algebraic determination.