Boundary states in boundary logarithmic CFT

TL;DR

This paper constructs boundary states in logarithmic conformal field theories, specifically for rank-2 Jordan cells in $c=-2$ LCFT, and explores their implications for string theory and the Verlinde formula.

Contribution

It provides explicit boundary Ishibashi and boundary states for rank-2 Jordan cells in $c=-2$ LCFT, advancing understanding of boundary conditions in logarithmic CFTs.

Findings

Constructed boundary Ishibashi states for rank-2 Jordan cells

Derived boundary states in the closed string picture for $c=-2$ LCFT

Discussed the Verlinde formula and applications to string theory

Abstract

There exist logarithmic CFTs(LCFTs) such as the $c_{p,1}$ models. It is also well known that it generally contains Jordan cell structure. In this paper, we obtain the boundary Ishibashi state for a rank-2 Jordan cell structure and, with these states in $c=-2$ rational LCFT, we derive boundary states in the closed string picture, which correspond to boundary conditions in the open string picture. We also discuss the Verlinde formula for LCFT and possible applications to string theory.