arXiv subjects
Publications and source records attributed to Richard Derryberry.
I define an algebraic metric and closed 3-form on a subspace $\mathcal{M}$ of the moduli of $G$-bundles on a complex projective curve $C$, and show that the resulting two-dimensional $σ$-model with target $\mathcal{M}$ has a zero-curvature formulation.
The central result of this paper is an identification of the shifted Cartier dual of the moduli stack $\mathcal{M}_{\mathfrak{g}}(C)$ of $\widetilde{G}$-Higgs bundles on $C$ of arbitrary degree (modulo shifts by $Z(\widetilde{G})$) with a quotient of the Langlands dual stack $\mathcal{M}_{^L\mathfrak{g}}(C)$. 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 stacks $\frac{\mathcal{M}_{\mathfrak{g}}(C)}Γ$ are observed to exist, which I conjecture to be the Coulomb branches for the 3d reduction of the 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$.