Algebraic \(K\)-theory and derived equivalences suggested by T-duality for torus orientifolds. (English) Zbl 1399.14011
Summary: 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 \(\mathbb{R}\) with no real points is (mildly) noncommutative.
MSC:
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 19E08 | \(K\)-theory of schemes |
| 19L64 | Geometric applications of topological \(K\)-theory |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 14F22 | Brauer groups of schemes |
| 14H60 | Vector bundles on curves and their moduli |
| 14H81 | Relationships between algebraic curves and physics |
Software:
DLMFReferences:
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