Supersymmetric Chern–Simons vortex systems and extended supersymmetric quantum mechanics algebras

Abstract

We study N = 2 supersymmetric Chern-Simons Higgs models in (2+1)-dimensions and the existence of extended underlying supersymmetric quantum mechanics algebras. Our findings indicate that the fermionic zero modes quantum system in conjunction with the system of zero modes corresponding to bosonic fluctuations, are related to an N = 4 extended 1-dimensional supersymmetric algebra with central charge, a result closely connected to the N = 2 spacetime supersymmetry of the total system. We also add soft supersymmetric terms to the fermionic sector in order to examine how this affects the index of the corresponding Dirac operator, with the latter characterizing the degeneracy of the solitonic solutions. In addition, we analyze the impact of the underlying supersymmetric quantum algebras to the zero mode bosonic fluctuations. This is relevant to the quantum theory of self-dual vortices and particularly for the symmetries of the metric of the space of vortices solutions and also for the non-zero mode states of bosonic fluctuations.

Localized fermions on domain walls and extended supersymmetric quantum mechanics

“…So in conclusion, there is no direct connection between global spacetime supersymmetry and SUSY QM algebras, at least in the context we used in this article. However, when the system possesses an initial N = 2, d = 3 global supersymmetry, an extended SUSY QM algebra underlies the system, see for example [23]. This is not however a general rule, but just an observation made for a particular system.…”

Higgs Phase in a Gauge U(1) Non-Linear CP1-Model. Two Species of BPS Vortices and Their Zero Modes

“…Replacement of the Maxwell kinetic term by the Chern-Simons density is also susceptible to being generalized to an extended supersymmetric gauge theory; see, e.g., [19]. In [20,21], the topological defects and structures of this last model have been thoroughly described. Moreover, this framework has been proven to play a role as an effective theory in describing graphene physics at Dirac points in [22].…”

Extended Supersymmetric Quantum Mechanics Algebras in Scattering States of Fermions off Domain Walls

“…However, there is no general rule that governs this result, that is, finding extended supersymmetric structures when many N = 2 are present in the initial system. In fact, there are cases in which the initial system does have N = 1 global supersymmetry and the quantum Hilbert space of the states has only one N = 2 SUSY QM algebra and not an extended one, as someone would suspect (see for example reference [25] and references therein).…”