September 9, 2019
TITLE: Global aspects of the 3d-3d correspondence
ABSTRACT: We discuss various aspects of the 3d supersymmetric quantum field theories obtained by compactifying a stack of M5 branes on a three-manifold, arising in the so-called “3d-3d correspondence.” In particular, we emphasize the role of higher-form symmetries of the M5 brane theory, which provide a refinement of the 3d-3d correspondence related to the global structure of the 3d gauge theories. We focus in particular on the case where the three-manifold is a Seifert manifold, where we write 3d Lagrangians for these theories. The vacuum equations take the form of Bethe-ansatz type equations, which we solve in several examples. This leads to new tests of the 3d-3d correspondence, in particular, of the action of the higher symmetry on the set of vacua. We comment on implications for the 3d-3d correspondence, arising from compactification on an associative cycle in a manifold.