Gapped gravitinos, isospin $\frac{\mathbf{1}}{2}$ particles, and $\mathcal{N}=2$ partial breaking

Abstract

Using results on topological band theory of phases of matter and discrete symmetries, we study topological properties of band structure of physical systems involving spin 1 2 and 3 2 fermions. We apply this approach to study partial breaking in 4D N = 2 gauged supergravity in rigid limit and we describe the fermionic gapless mode in terms of chiral anomaly. We study as well the homologue of the usual spin-orbit coupling L. S, that opens the vanishing band gap for free s = 1 2 fermions; and show that is precisely given by the central extension of the N = 2 supercurrent algebra in 4D spacetime. We also give comments on the rigid limit of Andrianopoli et al obtained in [28] and propose an interpretation of energy bands in terms of a chiral gapless isospin 1 2 -particle (iso-particle). Other features, such as discrete Tsymmetry in FI coupling space, effect of quantum fluctuations and the link with Nielson-Ninomiya theorem, are also studied.

't Hooft lines of ADE-type and topological quivers

“…The main ingredients of the 4D Chern-Simons theory are line and surface defects [45][46][47][48][49][50]; these topological quantities play a fundamental role in the study of this theory and the realisation of lower dimensional solvable systems. In particular, we distinguish two basic line operators: (i) Electrically charged Wilson lines which, roughly speaking, are assimilated to worldlines of particles in 2D space-time with a spectral parameter z related to rapidity; they are characterised by highest weights λ of representations R of the gauge symmetry G. (ii) Magnetically charged 't Hooft lines characterised by coweights µ of G and acting like Dirac monopoles.…”