Discrete integrable systems, supersymmetric quantum mechanics, and framed BPS states

Abstract

It is possible to understand whether a given BPS spectrum is generated by a relevant deformation of a 4D $$ \mathcal{N} $$ 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.

The threefold way to quantum periods: WKB, TBA equations and q-Painlevé

“…Analogous relations between 4d N = 2 gauge theories and discrete integrable systems were investigated in[103,104].…”