Mathematical Physics

Brane Webs in Type IIB String Theory can be used to engineer 5d N=1 gauge theories and SCFTs. These brane webs can also be used to obtain so called magnetic quivers, whose 3d Coulomb branches gives the Higgs branch of the 5d theory in question. We will see how to obtain these magnetic quivers for brane webs possibly in the presence of orientifold planes. Then we will see how 3d Coulomb branch technology (such as quiver subtraction) can be used to understand Higgsings and mass deformations of 5d SCFTs.

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The Hitchin systems are a remarkable family of integrable models associated to the moduli space of principal bundles on a compact Riemann surface. In this talk, I explain how the loop group uniformization of this moduli space can be used to construct an r-matrix for the Hitchin systems. This r-matrix has been previously used in the description of the Friedan-Schenker connection on the space of conformal blocks.

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