Quantum spin systems and supersymmetric gauge theories. Part I

The relation between supersymmetric gauge theories in four dimensions and quantum spin systems is exploited to find an explicit formula for the Jost function of the N site sl(2)X X X spin chain (for infinite dimensional complex spin representations), as well as the SLN Gaudin system, which reduces, in a limiting case, to that of the N-particle periodic Toda chain. Using the non-perturbative Dyson-Schwinger equations of the supersymmetric gauge theory we establish relations between the spin chain commuting Hamiltonians with the twisted chiral ring of gauge theory. Along the way we explore the chamber dependence of the supersymmetric partition function, also the expectation value of the surface defects, giving new evidence for the AGT conjecture.

Automated summary

By exploiting the relation between supersymmetric gauge theories and quantum spin systems, an explicit formula for the Jost function of the N site sl(2)X X X spin chain and the SLN Gaudin system has been found. Additionally, relationships between the spin chain commuting Hamiltonians and the twisted chiral ring of gauge theory have been established using non-perturbative Dyson-Schwinger equations. The research also explores the chamber dependence of the supersymmetric partition function and the expectation value of surface defects, offering new evidence for the AGT conjecture.