Frame-like gauge invariant Lagrangian formulation of massive fermionic higher spin fields in AdS3 space

Abstract

We construct the frame-like gauge-invariant Lagrangian formulation for massive fermionic arbitrary spin fields in three-dimensional AdS space. The Lagrangian and complete set of gauge transformations are obtained. We also develop the formalism of gauge-invariant curvatures for the massive theory under consideration and show how the Lagrangian is formulated in their terms. The massive spin-5/2 field is discussed as an example.

Supersymmetric Higher Spin Models in Three Dimensional Spaces

“…In this section, we review the Lagrangian description of the arbitrary spin bosonic fields in three-dimensional Minkowski and its cosmological extension AdS spaces [30]. Both for massless and massive fields, we present the gauge-invariant formulation using the frame-like field variables.…”

“…In particular, being completely antisymmetric on the world indices, it allows one to use the language of differential forms admitting, e.g., a coordinate-free description for the background Minkowski and anti de Sitter spaces (see below). For the three dimensions, this possibility has been realized in the papers [30,31]. The goal of this review is to present the general methods of supersymmetric Lagrangian construction for massive higher spin fields in 3D Minkowski and AdS spaces.…”

“…The goal of this review is to present the general methods of supersymmetric Lagrangian construction for massive higher spin fields in 3D Minkowski and AdS spaces. These methods are based on the gauge-invariant description of the massive fields [30,31] and are realized in the component approach for the case of on-shell N = 1 supersymmetry. The main content of this review is based on the papers [32,33].…”

Lagrangian formulation of the massive higher spin supermultiplets in three dimensional space-time

“…Naturally, this construction is based on the gauge invariant description for the massive d = 3 bosonic [30] and fermionic [31] higher spin fields developed in our previous works. 3 Recall that in d = 4 it was crucial for the whole construction that there exists the possibility to consider a kind 2 ), correspondingly.…”

“…Gauge invariant description of massive boson with spin s [30] requires massless fields with spins s ≥ l ≥ 0. Thus we introduce a collection of one-forms f α(2l) , Ω α(2l) , s − 1 ≥ l ≥ 1 as well as one-form A and zero-forms B αβ , π αβ and ϕ.…”