Week 02.11.2014 – 08.11.2014

Abelian gerbes play a ubiquitous role in string and supergravity theories. It is conjectured that non-abelian gerbe theories exist, but a satisfactory explicit construction of such a theory has not yet been achieved. Inspired by the possibility that a non-abelian theory of gerbes may be possible on non-conventional spacetimes, I will consider a toy model on a lattice that allows one to make some progress in this problem. In this talk, I will show how abelian gerbe theories may be described naturally on the lattice. I will outline a non-abelian generalisation and show how, under dimensional reduction, such theories give rise to lattice Yang-Mills.

F-theory paints a beautiful picture that relates gauge theories to purely geometric information, whereby the Dynkin diagrams of gauge groups come to life as 2-cycles of internal spaces. The caveat is that, such spaces are necessarily singular, and treating them sensibly requires resolving or deforming the singularities. Recently, my collaborator R. Savelli and I have proposed a new strategy that allows one to deal with singular spaces directly. It is based on Eisenbud’s so-called matrix factorisations. This remarkably simple concept has very deep connections to the mathematics of singularities. In this talk, I will review the basic notions needed to formulate the issues, assuming only standard knowledge of string theory. Then, after introducing our proposal, I will show examples of its applications, such as computations of chiral spectra for bound states of 7-branes.

Within the context of the duality between higher spin gravitational theories and a semi- classical limit of WN minimal models, we consider 2D CFTs with W1 symmetry at nite temperature, deformed by the presence of a chemical potential for the spin{three current. As a perturbative expansion in the chemical potential, we compute the Renyi and entanglement entropies for a single interval. The leading correction is universal and matches the holographic result, based on Wilson line functionals, obtained from the higher spin gravitational dual.