Title: Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I,
Abstract: It is possible to understand whether a given BPS spectrum is generated by a
relevant deformation of a 4D N=2 SCFT or of an asymptotically free theory from
the periodicity properties of the corresponding quantum monodromy. With the aim
of giving a better understanding of the above conjecture, in this paper we
revisit the description of framed BPS states of four-dimensional relativistic
quantum field theories with eight conserved supercharges in terms of
supersymmetric quantum mechanics. We unveil aspects of the deep
interrelationship in between the Seiberg-dualities of the latter, the discrete
symmetries of the theory in the bulk, and quantum discrete integrable systems.