Boundary States, Extended Symmetry Algebra and Module Structure for certain Rational Torus Models

TL;DR

This paper analyzes rational torus models with boundaries, constructing boundary states, deriving fusion rules, and exploring the extended symmetry algebra responsible for their rational structure.

Contribution

It explicitly constructs boundary states and the extended symmetry algebra for rational torus models with boundary conditions, revealing their module structure.

Findings

Boundary states are explicitly constructed for models with R^2=1/2k.

Fusion rules are derived from the boundary states using the Verlinde formula.

The chiral space decomposes into irreducible modules of the extended symmetry algebra.

Abstract

The massless bosonic field compactified on the circle of rational $R^2$ is reexamined in the presense of boundaries. A particular class of models corresponding to $R^2=\frac{1}{2k}$ is distinguished by demanding the existence of a consistent set of Newmann boundary states. The boundary states are constructed explicitly for these models and the fusion rules are derived from them. These are the ones prescribed by the Verlinde formula from the S-matrix of the theory. In addition, the extended symmetry algebra of these theories is constructed which is responsible for the rationality of these theories. Finally, the chiral space of these models is shown to split into a direct sum of irreducible modules of the extended symmetry algebra.