Higher form and higher group symmetries via mirror symmetry

Abstract

In this work we discuss a connection that relates the 1-form and the 2-group symmetries of 5D SCFTs derived from geometric engineering methods to monodromies of the corresponding B-models via mirror symmetry. Viewing defects as branes wrapping relative cycles in a non-compact CY3, we compute the VEVs of the relevant line operators and find that the defect groups can be read off from these VEVs expanded to the leading order. Via mirror map, we show concretely that the 1-form and the 2-group symmetries of the SCFT are related to the monodromy at the large radius point in the B-model. Additionally, we recursively obtain closed-form expressions of instanton expansions of the VEV of Wilson lines of certain 5D theories among which some have not been obtained so far using localization methods. We further conjecture that the 2-group symmetry is given by the Mordell-Weil torsion of the universal special geometry associated to the theory, generalizing the conjecture for rank-1 theories to all ranks.