B-Theory: Lecture & Eastern seminar 3

Wednesday 18 Nov 2020, 10:00 → 12:20 Europe/Moscow

Introduction to introduction to B-theory 3

The topic of this week -  Instantonic theories in dimensions  0, 1 and  2.  Based on works of Frenkel, Losev and Nekrasov.

We will discuss integral representation of the delta-form on a submanifold given by complete intersection of a set of functions. We will express it as a localization of a Q-supermanifold. We will specifically study smearing of the delta-form that later would be interpreted as a coupling constant. Then we will proceed with a one-dimensional example (example 2 of the previous talks). We will argue that quantum mechanical commutation relation between momentum and coordinate may be obtained without integral over infinite-dimensional space. Then we will go towards 2-dimensional theory that is off-shell formulation of Gromov-Witten theory. We will also explain how to get operator product expansion in such theories. This topic would be a base for 2-dimensional mirror symmetry of Frenkel and Losev (A-I-B) and its subsequent tropicalization, which we will study next week.

Rec (youtube)