Notes on D-branes and dualities in (p,q) minimal superstring theory

TL;DR

This paper analyzes boundary states in (p,q) minimal superstring theory, determining explicit forms of branes and their roles in duality, using modular bootstrap and superconformal field theory techniques.

Contribution

It provides a complete determination of Cardy states and boundary states in (p,q) minimal superstring theory, including their roles in dualities and consistency conditions.

Findings

Principal FZZT branes do not satisfy Cardy's conditions with each other.

Boundary states are explicitly constructed in both type 0A and 0B projections.

Principal FZZT branes act as order/disorder parameters in Kramers-Wannier duality.

Abstract

We study boundary states in (p,q) minimal superstring theory, combining the explicit form of matter wave functions. Within the modular bootstrap framework, Cardy states of (p,q) minimal superconformal field theory are completely determined in both cases of the different supercharge combinations, and the remaining consistency checks in the super-Liouville case are also performed. Using these boundary states, we determine the explicit form of FZZT- and ZZ-brane boundary states both in type 0A and 0B GSO projections. Annulus mplitudes of FZZT branes are evaluated and principal FZZT branes are identified. In particular, we found that these principal FZZT branes do not satisfy Cardy's consistency conditions for each other and play a role of order/disorder parameters of the Kramers-Wannier duality in spacetime of this superstring theory.