Mirror Symmetry and Spinor-Vector Duality: A Top-Down Approach to the Swampland Program

TL;DR

This paper explores mirror symmetry and Spinor-Vector Duality in string theory, proposing that SVD can distinguish between effective field theories that can or cannot be embedded in a UV-complete string framework.

Contribution

It introduces a top-down approach linking SVD to the Swampland program, suggesting SVD as a criterion for UV-completeness of EFTs derived from string theory.

Findings

SVD maps Wilson-line moduli in heterotic-string compactifications.

SVD serves as a potential boundary between consistent and inconsistent EFTs.

The approach connects worldsheet symmetries to low-energy effective theories.

Abstract

Mirror symmetry is one of the celebrated developments in pure mathematics that arose from an initial observation in worldsheet string constructions. The profound implications of mirror symmetry in the Effective Field Theory (EFT) limit of string compactifications was subsequently understood. In particular, it proved to be an exceptionally useful tool in the field of enumerative geometry. Spinor-Vector Duality (SVD) is an extension of mirror symmetry that can be readily understood in terms of the moduli parameters of toroidal heterotic-string compactifications, which include the metric, the anti-symmetric ternsor field and the Wilson-line moduli. While mirror symmetry corresponds to maps of the internal moduli parameters, {\i.e.} the metric and the anti-symmetric tensor field, SVD corresponds to maps of the Wilson-line moduli. Similar to mirror symmetry the imprint of SVD in the EFT limit can serve as a tool to study the properties of complex manifolds with vector-bundles. Spinor-Vector Duality motivates a top--down approach to the "Swampland" program, by studying the imprint of the symmetries of the worldsheet ultra-violet complete string constructions in the EFT limit. It is conjectured that SVD provides a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding in string theory versus those that do not.