Non-critical NSR string field theory and discrete states interaction in 2D supergravity

TL;DR

This paper develops a string field theory framework for non-critical NSR strings in 2D supergravity, revealing discrete states interactions and calculating related string amplitudes with specific pole structures.

Contribution

It constructs double-step picture changing operators and formulates supersymmetry transformations for D<10, providing new insights into discrete states in 2D supergravity.

Findings

String field theory for 2D supergravity coupled to matter is formulated.

Discrete set of primary fields and their poles are identified in string amplitudes.

Supersymmetry transformations form a closed on-shell algebra for D<10.

Abstract

String field theory for the non-critical NSR string is described. In particular it gives string field theory for the 2D super-gravity coupled to a $\hat{c}=1$ matter field. For this purpose double-step pictures changing operators for the non-critical NSR string are constructed. Analogues of the critical supersymmetry transformations are written for $D<10$, they form a closed on-shell algebra, however their action on vertices is defined only for discrete value of the Liouville momentum. For D=2 this means that spinor massless field has its superpartner in the NS sector only if its momentum is fixed. Starting from string field theory we calculate string amplitudes. These amplitudes for D=2 have poles which are related with discrete set of primary fields, namely 2R$\to$2R amplitude has poles corresponding to the n-level NS excitations with discrete momenta $p_1=n,~~p_2=-1\pm (n+1)$.