Organizing boundary RG flows

Abstract

We show how a large class of boundary RG flows in two-dimensional conformal field theories can be summarized in a single rule. This rule is a generalization of the 'absorption of the boundary spin'-principle of Affleck and Ludwig and applies to all theories which have a description as a coset model. We give a formulation for coset models with arbitrary modular invariant partition function and present evidence for the conjectured rule. The second half of the article contains an illustrated section of examples where the rule is applied to unitary minimal models of the A- and D-series, in particular the 3-state Potts model, and to parafermion theories. We demonstrate how the rule can be used to compute brane charge groups in the example of N=2 minimal models.

Figures (17)

• Figure 1: The geometrical representation of boundary conditions in the minimal model A-series.
• Figure 2: A pictorial representation of the flows \ref{['mmAflowI']} and \ref{['mmAflowII']} for $L_{1}<L',L_{1}+L'\leq k$: a single brane can flow to a superposition of point-like branes.
• Figure 3: A pictorial representation of the flows \ref{['mmAflowI']} and \ref{['mmAflowII']} for $L_{1}\geq L',L_{1}+L'\leq k$: a single brane can flow to a superposition of point-like branes.
• Figure 4: Pictorial representation of the flows \ref{['mmAflowIII']} and \ref{['mmAflowIV']}: a superposition of string-like branes can flow to a single brane.
• Figure 5: Ising model: flows from the free boundary condition to spin up or spin down.