Quantum toroidal integrable systems, 5d N=1 Super Yang-Mills and (p,q)-web diagrams in IIB string theory
Thu, Jun. 08th 2017, 14:15
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
Instanton partition functions of N=1 5d Super Yang-Mills reduced on S1 can be engineered in type IIB string theory from the (p,q)-branes web diagram. Branes intersections are associated to the (refined) topological vertex, while the $(p,q)$ diagram provides the gluing rules. Furthermore, the partition function is covariant under the action of a quantum toroidal algebra, the Ding-Iohara-Miki (DIM) algebra. In this talk, we present the construction of a web of representations in bijection with the $(p,q)$ web diagram. To each brane is associated a different representation (highest weight for D5, Fock for NS5), related through interwiners. These intertwiners generalize the fermionic presentation of the topological vertex to the refined case. They lead to the construction of a T-operator, for which the vacuum expectation value reproduces the instanton partition functions. With this method, it is also possible to obtain the qq- characters that encode the double quantization of the Seiberg-Witten curve.