Boundary Rings and N=2 Coset Models

TL;DR

This paper explores boundary states in N=2 coset models based on Grassmannians, revealing their geometric and algebraic structures, and analyzing the spectrum of boundary bound states within this framework.

Contribution

It establishes a connection between boundary states and the fusion ring of U(n), linking intersection geometry to quantum cohomology and quiver representations.

Findings

Intersection geometry is given by the fusion ring of U(n).

Boundary states correspond to critical points of a boundary superpotential.

Rational boundary CFT produces a limited subset of quiver representations.

Abstract

We investigate boundary states of N=2 coset models based on Grassmannians Gr(n,n+k), and find that the underlying intersection geometry is given by the fusion ring of U(n). This is isomorphic to the quantum cohomology ring of Gr(n,n+k+1), and thus can be encoded in a ``boundary'' superpotential whose critical points correspond to the boundary states. In this way the intersection properties can be represented in terms of a soliton graph that forms a generalized, Z_{n+k+1} symmetric McKay quiver. We investigate the spectrum of bound states and find that the rational boundary CFT produces only a small subset of the possible quiver representations.