Mirror symmetry and spinor-vector duality

by Alon Faraggi

Friday 24 Mar 2023, 11:30 → 13:30 Europe/Zurich

4/2-037 - TH meeting room (CERN)

Mirror symmetry was first observed in worldsheet string constructions and shown to have important implications in the effective field theory 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 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 couple 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. In the talk I will describe how the spinor-vector duality was discovered, its relation to mirror symmetry and possible directions of future mathematical research, some of which are analogous to similar aspects in mirror symmetry.