ZZ branes from a worldsheet perspective

TL;DR

This paper explores how non-compact ZZ branes arise as limits of compact FZZT branes in minimal models coupled to 2D quantum gravity, revealing a unified boundary state structure.

Contribution

It demonstrates the emergence of ZZ branes as limits of FZZT branes and shows all ZZ boundary states derive from a basic (1,1) state combined with Cardy states.

Findings

ZZ branes emerge as limits of FZZT branes under specific conditions

All ZZ boundary states can be constructed from the basic (1,1) boundary state

A unified perspective on boundary states in minimal models coupled to gravity

Abstract

We show how non-compact space-time (ZZ branes) emerges as a limit of compact space-time (FZZT branes) for specific ratios between the square of the boundary cosmological constant and the bulk cosmological constant in the (2,2m - 1) minimal model coupled to two-dimensional euclidean quantum gravity. Furthermore, we show that the principal (r,s) ZZ brane can be viewed as the basic (1,1) ZZ boundary state tensored with a (r,s) Cardy boundary state for a general (p,q) minimal model coupled to two-dimensional quantum gravity. In this sense there exists only one ZZ boundary state, the basic (1,1) boundary state.