Spinor-Vector Duality and Mirror Symmetry

Abstract

Mirror symmetry was first observed in worldsheet string constructions and shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi-Yau manifolds. It opened up a new field in pure mathematics and was utilised in the area of enumerative geometry. Spinor-Vector Duality (SVD) is an extension of mirror symmetry. This can be readily understood in terms of the moduli of toroidal compactification of the heterotic string, which include the metric the antisymmetric tensor field and the Wilson line moduli. In terms of toroidal moduli, mirror symmetry corresponds to mappings of the internal space moduli, whereas spinor-vector duality corresponds to maps of the Wilson line moduli. In the past few of years, we demonstrated the existence of spinor-vector duality in the effective field theory compactifications of the string theories. This was achieved by starting with a worldsheet orbifold construction that exhibited spinor-vector duality and resolving the orbifold singularities, hence generating a smooth effective field theory limit with an imprint of the spinor-vector duality. Just like mirror symmetry, the spinor-vector duality can be used to study the properties of complex manifolds with vector bundles. Spinor--vector duality offers a top-down approach to the ``Swampland''-program, by exploring the imprint of the symmetries of the ultra-violet complete worldsheet string constructions in the effective field theory limit. The SVD suggests a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding versus those that do not.

arXiv comment15 pages. 2 figures. Contribution to Universe Special Issue: Particle Physics and Cosmology: A Themed Issue in Honour of Professor Dimitri Nanopoulos. Published version

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• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme