In 2005 Kapustin and Witten reformulated the geometric Langlands program to the language of quantum field theory. In the process, they conjectured a categorical equivalence between certain branes (boundary conditions of QFTs) which are compatible with several topological twists on hyperkaehler manifolds. In this talk, first I will introduce BBB and BAA branes and their conjectured equivalence on the Higgs moduli space. Then, I will explain a simple setting, the case of the semi-flat hyperkaehler metric, which approximates the Hitchin metric and in which the equivalence can be approached and a simplified duality between BBB and BAA branes can be proven.
Semi-flat mirror symmetry of hyperkaehler metrics and branes
01.12.2022 09:45 - 11:15
Organiser:
A. Mellit, B. Szendroi, V. Vertesi
Location: