We investigate the different large N phases of a deformed Gross-Witten-Wadia U(N) matrix model. The deformation, which leads to a solvable model, corresponds to the addition of characteristic polynomial insertions and mimicks the one-loop determinant of fermion matter. In one version of the model, the GWW phase transition is smoothed out and it becomes a crossover. In another version, the phase transition occurs along a critical line in the two-dimensional parameter space spanned by the 't~Hooft coupling $\lambda $ and the Veneziano parameter $\tau $. A calculation of the $\beta $ function shows the existence of an IR stable fixed point. ---- 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.

Gauged supergravities arise from consistent truncations of string theory and provide a solid framework for condensed matter applications, in a context where the dual field theory is well understood. In this talk we shall discuss different models, including p-wave superconductivity by condensation of a two-form potential.

The exact string coupling dependence of higher derivative terms in the type IIA and type IIB effective action is highly constrained by a combination of duality symmetries and by results from perturbative string theory. For example, we show that terms of the form D to the 2k times R to the 4th in type IIA theory should receive no perturbative contributions beyond genus k (k greater than 0). We also propose that the exact modular functions of general type IIB higher derivative terms are determined by a Poisson equation on the fundamental domain of the moduli space.