Stacky dualities for the moduli of Higgs bundles

The central result of this paper is an identification of the shifted Cartier dual of the moduli stack M-g(C) of (G) over tilde -Higgs bundles on C of arbitrary degree (modulo shifts by Z((G) over tilde)) with a quotient of the Langlands dual stack MLg(C). Via hyperkahler 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 stacks M-g(c)/Gamma are observed to exist, which I conjecture to be the Coulomb branches for the 3d reduction of the 4d V = 2 theories of class S. (C) 2020 Elsevier Inc. All rights reserved.