Generalized Kähler manifolds, and their twisted counterparts, are equivalent to the bihermitian manifolds discovered by Sylvester James Gates, Chris Hull and Martin Roček in the context of 2-dimensional supersymmetric quantum field theories in 1984.
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These structures first arose in Hitchin's program of characterizing geometrical structures via functionals of differential forms, a connection which formed the basis of Robbert Dijkgraaf, Sergei Gukov, Andrew Nietzke and Cumrun Vafa's 2004 proposal that topological string theories are special cases of a topological M-theory.
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