# R-matrix formalism for qq-characters in gauge theories

09.12.2022 10:00

qq-characters can be viewed in two ways. From physics point of view they are certain observables in supersymmetric gauge theories with

eight supercharges having special regularity properties. Two q letters indicate two deformation parameters of the Omega-backgraound in which the gauge theory lives. This approach has been studied a lot in the works of N. Nekrasov.

From a representation theoretic perspective, pioneered by E. Frenkel and N. Reshetikhin, qq-characters are deformations of q-characters. The latter are traces of R-matrices of quantum affine Lie algebras U_q(g) in finite-dimensional representations. However, after the deformation the nice R-matrix interpretation seems to be lost.

In our work we propose a very different R-matrix formalism for qq-characters involving a quantum toroidal (double affine) algebra. The qq-character is no longer a trace, but instead a matrix element of the corresponding R-matrix. The type of the character depends both on the representation in which the R-matrix is evaluated and the external states of the representation defining the matrix element.

We provide several examples of qq-characters corresponding to classical series of root systems. We also relate our calculations to refined topological strings and 5-brane webs in Type IIB string theory.

This talk is based on a joint work with Mehmet Batu Bayindirli, Dilan Demirtas and Can Kozcaz.

### Lieu

Bâtiment: Conseil Général 7-9

Room 6-13, Séminaire "Physical Mathematics Seminar Series"

### Organisé par

Section de mathématiques### Intervenant-e-s

Yegor Zenkevich, SISSAentrée libre