U2, Aula 5017
Title: Chord diagrams for Schur indices
Abstract: Recently, a new correspondence was conjectured between half Schur indices of the pure 4d SU(2) N=2 supersymmetric Yang-Mills (SYM) theory with line operator insertions and partition functions of the Sachdev-Ye-Kitaev (SYK) model in the double scaling limit (DSSYK). Motivated by this, we explore a generalization to SU(N) N=2 SYM theories. We discuss the algebra A_Schur of line operators, focusing in particular on the Wilson lines, and show how it can be represented in terms of q-deformed harmonic oscillators. In this framework, the half Schur indexadmits a natural description as an expectation value in the Fock space of the oscillators. This q-oscillator perspective further suggests an interpretation in terms of colored chord diagrams that generalize the ones of DSSYK, and maps the half index to a purely combinatorial quantity. Finally, we establish a connection with Toda quantum mechanics, an integrable system whose Hamiltonians we show coincide with the Wilson lines of the SU(N) SYM.