The Clifford monopole equations

Ponente(s): Rafael Herrera Guzmán, Noemi Santana, Alexander Quintero

The spin group and spin algebra have, for a long time, played a very important role in Differential Geometry and Physics. In the search for a unified spinorial approach to special Riemannian holonomy, we found twisted pure spinors which generalize the classical pure spinor developed by Cartan. Along the way, we discovered that parallel twisted pure spinors, besides characterizing the special Riemannian holonomies, satisfy the corresponding twisted Dirac equation and a curvature identity. These pair of equations constitute the Clifford monopole equations which generalize, to higher dimensions, the 4D Seiberg-Witten equations. Their solutions (modulo gauge equivalence) define a moduli space to which the Atiyah-Jeffrey-Mathai-Quillen formalism can be applied to calculate the partition function of a topological quantum field theory.