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Twisted derived equivalences and string theory dualities with B-field

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KA2W03 - Mathematical physics: algebraic cycles, strings and amplitudes

It’s well-known that D-branes on a type IIB string theory compactified onan algebraic variety X (usually a Calabi-Yau variety) are classified by the(bounded) derived category D(X) of coherent sheaves on X.  Thus dualitiesbetween string theories on two varieties X and Y are manifested byequivalences D(X) ≅ D(Y).  For orientifold string theories with non-trivialB-field, the situation is more complicated, and sometimes D(X) has to be replacedby D(X, α), where α is a nontrivial class in the Brauer group.  We discusscases where string theory dualities are reflected in equivalences ofderived equivalences of categories of twisted coherent sheaves,as well as interesting possible purely algebraic generalizations. This is based in part on joint work with Charles Doran, Andreas Malmendier and Stefan Mendez-Diez, andwith Niranjan Ramachandran.

This talk is part of the Isaac Newton Institute Seminar Series series.

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