Induced Boundary Flow on the c = 1 Orbifold Moduli Space

TL;DR

This paper investigates how boundary conditions in a specific 2D conformal field theory change under bulk perturbations, demonstrating the consistency of boundary flows and calculating the decrease in ground state multiplicity.

Contribution

It extends the understanding of boundary flows in the $c=1$ orbifold CFT, showing their consistency under bulk marginal operators and computing the ground state multiplicity reduction.

Findings

Boundary flow is consistent for any bulk marginal operator.

Ground state multiplicity decreases under the flow.

Results extend to the supersymmetric $c=3/2$ case.

Abstract

Boundary flow in the $c=1$ 2d CFT of a $\mathbb{Z}_2$ orbifold of a free boson on a circle is considered. Adding a bulk marginal operator to the $c=1$ orbifold branch induces a boundary flow. We show that this flow is consistent for any bulk marginal operator and known initial given boundary condition. The supersymmetric $c=3/2$ case is also mentioned. The supersymmetric $c=3/2$ case is also mentioned. For the circle branch of the moduli space this has been shown in arXiv:hep-th/0609034v2. The ground state multiplicity ($g_b$) is calculated and it is shown that it does indeed decrease.