A string field theoretical description of (p,q) minimal superstrings

TL;DR

This paper develops a string field theory for (p,q) minimal superstrings using a free-fermion realization of the 2cKP hierarchy, connecting matrix models, algebraic curves, and super Liouville theory.

Contribution

It introduces a novel string field theory framework for (p,q) minimal superstrings, linking matrix models, algebraic curves, and super Liouville theory, and clarifies subtle points like flux quantization.

Findings

Algebraic curves for disk amplitudes and partition functions match known superstring results.

Virasoro constraints incorporate quantized fluxes naturally.

Type 0A superstrings derived via orbifolding from type 0B strings.

Abstract

A string field theory of (p,q) minimal superstrings is constructed with the free-fermion realization of 2-component KP (2cKP) hierarchy, starting from 2-cut ansatz of two-matrix models. Differential operators of 2cKP hierarchy are identified with operators in super Liouville theory, and we obtain algebraic curves for the disk amplitudes of \eta=-1 FZZT-branes and the partition functions of neutral/charged \eta=-1 ZZ branes, which correctly reproduce those of type 0B (p,q) minimal superstrings in conformal backgrounds. In the course of study, some subtle points are clarified, including a difference of (p,q) even/odd models and quantization of flux, and we show that the Virasoro constraints naturally incorporate quantized fluxes without ambiguity. We also argue within this string field framework that type 0A minimal superstrings can be obtained by orbifolding the type 0B strings with a Z_2 symmetry existing when special backgrounds are taken.