Localized fermions on domain walls and extended supersymmetric quantum mechanics

Abstract

We study fermionic fields localized on topologically unstable domain walls bounded by strings in a grand unified theory theoretical framework. Particularly, we found that the localized fermionic degrees of freedom, which are up and down quarks as well as charged leptons, are connected to three independent N = 2, d = 1 supersymmetric quantum mechanics algebras. As we demonstrate, these algebras can be combined to form higher order representations of N = 2, d = 1 supersymmetry. Due to the uniform coupling of the domain wall solutions to the down-quarks and leptons, we also show that a higher order N = 2, d = 1 representation of the down-quark-lepton system is invariant under a duality transformation between the couplings. In addition, the two N = 2, d = 1 supersymmetries of the down-quark-lepton system, combine at the coupling unification scale to form an N = 4, d = 1 supersymmetry. Furthermore, we present the various extra geometric and algebraic attributes that the fermionic systems acquire, owing to the underlying N = 2, d = 1 algebras.

Localized Fermions on Superconducting Domain Walls and Extended Supersymmetry with Non-trivial Topological Charges

“…In addition, the system also has three distinct N = 4, d = 1 supersymmetries, with non-trivial topological charges, as can be seen in Table 2 In addition, we studied some dualities of the one dimensional superalgebras we found. The present work is a generalization of a previous work [4], where we found that a N = 4, d = 1 supersymmetry underlies the fermionic system that is composed by the lepton and down quark, in the particular case of gauge coupling unification. We believe that the work we presented in the present article generalizes the work of the previous one and also motivates some questions, with regards the existence of non-trivial topological charges.…”

“…In a previous paper [4] we demonstrated that the fermionic zero modes localized on topologically unstable domain walls bounded by strings in a grand unified theory theoretical framework, can be connected to three independent N = 2, d = 1 supersymmetric quantum mechanics algebras (for reviews and important papers on supersymmetry see [?, 5-14]). The fermions we took into account were up quarks, down quarks and also charged leptons.…”

“…In this letter we actually found an enhanced supersymmetry of the field theory but not of the S-matrix of the model and we believe that this enhanced symmetry containing non-trivial supercharges, can be an indication of a more involved symmetry yet to be found. This paper is organized as follows: In section 1 we briefly review all the necessary information concerning fermions on a domain wall and their connection to the three distinct N = 2, d = 1 supersymmetries, following reference [4]. In addition we shall also present the theoretical framework of the domain wall model we shall use.…”

On the position dependent effective mass Hamiltonian

“…Such an elegant method is given in [38]. First, let us recall the general form of RE [38][39][40][41][42][43][44][45][46], which is given by dK dx…”

Modular Operators and Entanglement in Supersymmetric Quantum Mechanics

“…Supersymmetric (SUSY) quantum mechanics [1] has shown to be a useful arena in which to invesitigate various mathematical and physical properties of symmetry operators throughout diverse fields of theoretical physics [2][3][4][5][6]. Here, we extend the available symmetry operators to include the modular operators first introduced by Tomita and Takesaki [7].…”