MS Seminar (Mathematics - String Theory)

Speaker: Piljin Yi (KIAS)
Title: part 1: Algebra, Geometry, and Hydrogen Atom
part 2: Wall-Crossing and Quiver Invariant
Date: Tue, Nov 20, 2012, 13:15 - 14:45
Place: Seminar Room A
Related File: 777.pdf
Abstract: part 1: Algebra, Geometry, and Hydrogen Atom

In this first introductory part, we review how geometry and quantum states are tightly connected in string theory. In particular, this leads to the wall-crossing problem where (non-)existence of so-called calibrated cycles can be figured out by solving relatively simple class of Schroedinger problems, or vice versa.

part 2: Wall-Crossing and Quiver Invariant

We start with a one-slide review of the Kontsevich-Soibelman (KS) solution to the wall-crossing problem and then proceed to direct and comprehensive physics counting of BPS states that eventually connects to KS. We also asks what input data is needed for either approaches to produce complete BPS spectra, and this naturally leads to the BPS quiver representation of BPS states and the new notion of quiver invariants.

We propose a simple geometrical conjectures that can segregate BPS states in Higgs phases of the BPS quiver dynamics to those that experience wall-crossing and those that do not, and give proofs for all cyclice Abelian quivers. We close with explanation of how physics distinguishes two such classes of BPS states.