Boundary RG Flows of N=2 Minimal Models

TL;DR

This paper investigates boundary renormalization group flows in N=2 minimal models through Landau-Ginzburg methods, identifying flow patterns, operators, and charge lattices for B- and A-branes, revealing their algebraic and topological structures.

Contribution

It introduces an algebraic matrix relation approach to analyze boundary RG flows and determines the charge lattices of B- and A-branes in N=2 minimal models.

Findings

Charge lattice of B-branes is Z_{k+2}.

Charge lattice of A-branes is Z^{k+1}.

Flow patterns and operators generating boundary RG flows are characterized.

Abstract

We study boundary renormalization group flows of N=2 minimal models using Landau-Ginzburg description of B-type. A simple algebraic relation of matrices is relevant. We determine the pattern of the flows and identify the operators that generate them. As an application, we show that the charge lattice of B-branes in the level k minimal model is Z_{k+2}. We also reproduce the fact that the charge lattice for the A-branes is Z^{k+1}, applying the B-brane analysis on the mirror LG orbifold.