|M.Sc Student||Nazzal Belal|
|Subject||Integrable Models and the Index of E-string|
|Department||Department of Physics||Supervisor||Dr. Shlomo S Razamat|
We study four dimensional supersymmetric theories obtained by compactifications of six dimensional theories on a Riemann surface. There is large class of theories in four dimensions that can be engineered in this way and this construction can lead to various insights into the physics in four dimensions. One particular example is relating certain class of surface defects in four dimensional theories and quantum mechanical integrable models.
Surface defects are non-local operators that can arise in quantum field theory. One way to introduce such defects in a theory is by triggering an RG flow with a spacetime dependent vacuum expectation value. In supersymmetric theories, when one computes the superconformal index of a theory with defect, the result can be obtained by acting with a difference operator on the index of the theory without defect. These difference operators happen often to be related to Hamiltonians of quantum mechanical integrable models.
In this thesis, we study a certain case of such relations. We consider four dimensional theories obtained as a compactification of six-dimensional theory known as the E-string, and we show that it is related to a quantum integrable model known as the van Diejen model.