We discuss the 5d AGT correspondence of supergroup gauge theories with A-type
    supergroups. We introduce two intertwiners called positive and negative
    intertwiners to compute the instanton partition function. The positive
    intertwiner is the ordinary Awata-Feigin-Shiraishi intertwiner while the
    negative intertwiner is an intertwiner obtained by using central charges with
    negative levels. We show that composition of them gives the basic Nekrasov
    factors appearing in supergroup partition functions. We explicitly derive the
    instanton partition functions of supergroup gauge theories with A and D-type
    quiver structures. Using the intertwiners, we briefly study the Gaiotto state,
    $qq$-characters and the relation with quiver W-algebra. Furthermore, we show
    that the negative intertwiner corresponds to the anti-refined topological
    vertex recently defined by Kimura and Sugimoto. We also discuss how superquiver
    theories should appear in our formalism if they exist. The existence of the AGT
    correspondence of the theories we study in this paper implies that there is a
    broader 2d/4d (5d/$q$-algebra) correspondence, or more generally the BPS/CFT
    correspondence, where new non-unitary theories play important roles.

    Source link


    Leave A Reply