Non-Lagrangian theories from brane junctions

Abstract

In this article we use 5-brane junctions to study the 5D T N SCFTs corresponding to the 5D N = 1 uplift of the 4D N = 2 strongly coupled gauge theories, which are obtained by compactifying N M5 branes on a sphere with three full punctures. Even though these theories have no Lagrangian description, by using the 5-brane junctions proposed by Benini, Benvenuti and Tachikawa, we are able to derive their Seiberg-Witten curves and Nekrasov partition functions. We cross-check our results with the 5D superconformal index proposed by Kim, Kim and Lee. Through the AGTW correspondence, we discuss the relations between 5D superconformal indices and n-point functions of the q-deformed W N Toda theories.

Topological vertex for Higgsed 5d T N theories

“…The claim of [21,22,24,25] is that the correct partition function of the 5d field theory can be computed from the topological string partition function by appropriately cancelling these contributions, namely the 5d Nekrasov partition function has the following form…”

“…We start by recalling the usual rule for the identification of decoupled factors in a toric diagram which is more easily described in the M-theory dual [21,22] can be identified as the contributions coming from M2-branes wrapping curves with zero intersection number with any compact divisor of the geometry. In particular these curves can be continuously moved off to infinity and the states carry charge only under global symmetries of the 5d theory.…”

“…be computed by the powerful technique of the refined topological vertex [19,20] after eliminating what we call decoupled factor which is a contribution associated to strings between parallel external legs [21,22,25]. Technical details of the refined topological vertex as well as the decoupled factor are summarised in appendix A.…”

“…After the removal of some extra factors independent of the Coulomb branch moduli it was possible to compute the partition function of the T N theory [21,22]. The enhancement of the flavour symmetries in its superconformal index 3 was also checked in [14,21,22], and a crucial point in obtaining enhancement of the global symmetry of five-dimensional superconformal field theories was the correct removal of the extra factors independent of the Coulomb branch moduli [12,14,21,22,[24][25][26][27][28]. 4 On the other hand the web diagrams corresponding to Higgsed 5d T N theories are not dual to toric geometries and therefore simple application of the refined topological vertex does not work.…”

“…We can first try to compute the result by simply applying the topological vertex to the Higgsed web diagram of the right figure of figure 8. Since the Higgsed web diagram consists of a single T 2 diagram 11 it is possible to compute the topological string partition function performing all Young diagram summations and the result is simply [21,22,42] …”