The central result of this paper is an identification of the shifted Cartier dual of the moduli stack Mg(C) of G-Higgs bundles on C of arbitrary degree (modulo shifts by Z( G)) with a quotient of the Langlands dual stack ML g (C). Via hyperkähler rotation, this may equivalently be viewed as the identification of an SYZ fibration relating Hitchin systems for arbitrary Langlands dual semisimple groups, coupled to nontrivial finite B-fields. As a corollary certain self-dual stacksare observed to exist, which I conjecture to be the Coulomb branches for the 3d reduction of the 4d N = 2 theories of class S.
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