Algebraic K-theory and derived equivalences suggested by T-duality for torus orientifolds

TL;DR

This paper explores algebraic K-theory and derived category equivalences inspired by T-duality in string theory, revealing a Mukai duality involving noncommutative structures for real algebraic varieties.

Contribution

It establishes algebraic analogues of T-duality isomorphisms using algebraic K-theory and derived categories, including a novel noncommutative Mukai duality for real genus-1 curves.

Findings

Isomorphisms of twisted KR-groups have algebraic counterparts.

Derived category equivalences correspond to T-duality transformations.

A noncommutative Mukai duality is identified for certain real algebraic curves.

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.