Spherical Hecke algebra in the Nekrasov-Shatashvili limit and N=2 instanton partition function

by Dr Jean Emile Bourgine (INFN - Bologna)

Wednesday 4 Feb 2015, 15:00 → 16:00 Europe/Rome

Aula Teorici (Dipartimento di Fisica e Astronomia)

Instanton partition functions of $\mathcal{N}=2$ gauge theories manifest remarquable properties. In particular, they exhibit both integrable features and an intriguing correspondence (AGT) with 2d Conformal Field Theories (Liouville&Toda). This can be understood from the presence of the Spherical Hecke central algebra, a Hopf algebra built upon a Double Degenerate Affine Hecke Algebra. In this talk, I will review the action of the algebra on Nekrasov partition functions. Then, I will consider a specific limit of the background where integrability becomes explicit and takes the form of a TBA-like Non-Linear Integral Equation.