Boundary Structure and Module Decomposition of the Bosonic $Z_2$ Orbifold Models with $R^2=1/2k$

TL;DR

This paper analyzes boundary structures and module decompositions in bosonic Z2 orbifold models with specific radii, providing a new free field representation of boundary states and clarifying the algebraic module structure.

Contribution

It introduces a novel free field representation of boundary states and identifies modules of the extended symmetry algebra in Z2 orbifold models with R^2=1/2k.

Findings

Derived a consistent partition function splitting

Constructed a free field boundary state representation

Identified algebra modules within the state space

Abstract

The $Z_2$ bosonic orbifold models with compactification radius $R^2=1/2k$ are examined in the presence of boundaries. Demanding the extended algebra characters to have definite conformal dimension and to consist of an integer sum of Virasoro characters, we arrive at the right splitting of the partition function. This is used to derive a free field representation of a complete, consistent set of boundary states, without resorting to a basis of the extended algebra Ishibashi states. Finally the modules of the extended symmetry algebra that correspond to the finitely many characters are identified inside the direct sum of Fock modules that constitute the space of states of the theory.