Beyond Algebraic Superstring Compactification: Part II

TL;DR

This paper discusses extending superstring compactification frameworks beyond algebraic methods, emphasizing heterotic models and mirror duality in complex and symplectic geometries.

Contribution

It proposes a more general, non-algebraic approach to superstring models that aligns with mirror duality, moving beyond traditional algebraic geometry methods.

Findings

Identifies limitations of algebraic models in superstring compactification.

Suggests non-algebraic deformations compatible with mirror duality.

Highlights the need for heterotic frameworks in superstring analysis.

Abstract

The most impressively prolific exploration of superstring models (aiming for our physical reality) has been focused on worldsheet-supersymmetric gauged linear sigma models and the closely associated complex-algebraic toric geometry. Mirror duality relates this to the inherently real symplectic geometry of Calabi-Yau factors in spacetime, implying a need for a more general, heterotic framework of analysis. In turn, a closer look at possible deformations even amongst the complex-algebraic complete intersections and toric geometry models themselves indicates an a priori non-algebraic type of generalization that however perfectly aligns with requirements of mirror duality.