SU(1, 1|N) superconformal mechanics with fermionic gauge symmetry

Abstract

Abstract:We study superpaticle models with fermionic gauge symmetry on the coset spaces of the SU(1, 1|N ) supergroup. We first construct SU(1, 1|N ) supersymmetric extension of a particle on AdS 2 possessing the κ-symmetry. Including angular degrees of freedom and extending this model to a superparticle on the AdS 2 × CP N −1 background with two-form flux, one breaks the κ-symmetry down to a fermionic gauge symmetry with one parameter. A link of the background field configuration to the near horizon black hole geometries is discussed.

Superfield approach to higher derivative $$ \mathcal{N} $$ = 1 superconformal mechanics

“…where Λ is an arbitrary function. The Taylor expansion of the function (22) in the Grassmannodd variables can be divided into two parts…”

On OSp(N |2) superconformal mechanics

“…In the present paper, we extend the analysis of [26] to the osp(N|2) superalgebra. The isntance N = 4 is special.…”

“…This proposal inspired extensive studies [8]- [24], which proved useful for understanding the structure of interactions of N = 4 supermultiplets of su(1, 1|2), osp(4|2) and D(2, 1; α). Some of these models are described by the κ-symmetric actions [11,15,26].…”

“…Superconformal mechanics can also be constructed by higher-dimensional reduction [27,28]. Finally, by using the method of nonlinear realizations one can directly build the action, whose form can be restricted by requiring the κ-symmetry [11,12,15,25,26,29,30]. In a recent paper [26], this method was applied for the construction of superpaticle models on the coset spaces of the SU(1, 1|N) supergroup.…”

“…Remarkably enough, the coset of OSp(4|2) supergroup with the bosonic part AdS 2 × S 2 is also of particular interest from the superfield standpoint, as it represents the only superextension of AdS 2 ×S 2 which admits a superconformally flat supervielbein and superconnections [33]. For generic N the κ-symmetry is broken down to a one-parametric gauge symmetry in analogy with [26]. A remarkable fact, however, is that the Hamiltonian structure remains the same as in the N = 4 case, because the additional fermionic degrees of freedom show up in second class constraints only.…”