Algebraic K-theory and derived equivalences suggested by T-duality for torus orientifolds
arXiv:1604.04535 · doi:10.1016/j.jpaa.2016.12.025
Abstract
We show that certain isomorphisms of (twisted) KR-groups that underlie T-dualities of torus orientifold string theories have purely algebraic analogues in terms of algebraic K-theory of real varieties and equivalences of derived categories of (twisted) coherent sheaves. The most interesting conclusion is a kind of Mukai duality in which the "dual abelian variety" to a smooth projective genus-1 curve over R with no real points is (mildly) noncommutative.
15 pages, based on a talk at the conference on K-theory, Cyclic Homology and Motives, Rutgers, 2015