5d N=1 Super Yang-Mills, (p,q)-web diagrams in IIB string theory and quantum toroidal integrable systems

by Dr Jean Emile Bourgine (KIAS, Seoul SOUTH Korea)

Tuesday 7 Nov 2017, 15:00 → 16:00 Europe/Rome

Aula Teorici (Dipartimento di Fisica e Astronomia)

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 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. In fact, this T-operator is the Baxter operator of a new class of integrable systems characterized by a quantum toroidal algebra (an affine version of the usual quantum groups). With this method, it is also possible to obtain the qq-characters that encode the double quantization of the Seiberg- Witten curve.