4d mirror brane for twisted cotangent bundle T*G // L_I

Establish that, for any subset I of simple roots of the connected semisimple algebraic group G, the twisted cotangent bundle T*G // L_I (the cotangent bundle of the homogeneous space G/L_I) is 4d mirror dual to T*{G} //_{e_I} U, where {G} is the Langlands dual group, e_I is the regular nilpotent element associated to the Levi subgroup L_I, and U is the maximal unipotent subgroup of {G}.

Background

The paper studies intersections of twisted cotangent bundles and their expected duals under symplectic duality and S-duality. In the final section, the authors aim to expand known families of 4d mirror branes and connect them to constructions from quiver gauge theories and relative Langlands duality.

Building on examples such as bow varieties and parabolic Slodowy varieties, they propose mirror correspondences beyond the standard parabolic/Borel cases. Specifically, they conjecture a new pairing between the cotangent bundle of G/L_I and a unipotent-twisted cotangent bundle of the Langlands dual group involving the regular nilpotent e_I. This fits their broader program of identifying mirror brane pairs whose intersections yield known 3d mirror varieties.