Non-Critical Strings, Del Pezzo Singularities And Seiberg-Witten Curves

TL;DR

This paper explores limits of type II Calabi-Yau compactifications with singularities, relating them to non-critical strings with E8 symmetry, and connects their moduli spaces to Seiberg-Witten curves and special geometry.

Contribution

It introduces a framework for decoupling subsectors of string theory to study intrinsically stringy BPS spectra and links geometric moduli spaces to Seiberg-Witten curves with elliptic singularities.

Findings

Identification of decoupled subsectors with stringy BPS spectra

Connection between moduli spaces and special geometry of non-compact Calabi-Yaus

Representation of moduli spaces via Seiberg-Witten curves with elliptic singularities

Abstract

We study limits of four-dimensional type II Calabi-Yau compactifications with vanishing four-cycle singularities, which are dual to $\IT^2$ compactifications of the six-dimensional non-critical string with $E_8$ symmetry. We define proper subsectors of the full string theory, which can be consistently decoupled. In this way we obtain rigid effective theories that have an intrinsically stringy BPS spectrum. Geometrically the moduli spaces correspond to special geometry of certain non-compact Calabi-Yau spaces of an intriguing form. An equivalent description can be given in terms of Seiberg-Witten curves, given by the elliptic simple singularities together with a peculiar choice of meromorphic differentials. We speculate that the moduli spaces describe non-perturbative non-critical string theories.