Abstract
We consider unconstrained formulation of the higher spin gauge theory in anti--de Sitter (AdS) spacetime, given by actions [A. Y. Segal, arXiv:0103028; M. Najafizadeh, Phys. Rev. D 98, 125012 (2018)], and provide on-shell supersymmetry transformations for the $\mathcal{N}=1$ unconstrained massless higher spin supermultiplet in four-dimensional ${\mathrm{AdS}}_{4}$. Such an irreducible supermultiplet $({\mathrm{\ensuremath{\Phi}}}_{1},{\mathrm{\ensuremath{\Phi}}}_{2};{\mathrm{\ensuremath{\Psi}}}_{1},{\mathrm{\ensuremath{\Psi}}}_{2})$ contains a pair of bosonic fields, with opposite parity, which are generating functions (infinite collection of totally symmetric real tensor fields of all integer rank $s=0,1,\dots{},\ensuremath{\infty}$), as well as two fermionic fields, which have opposite signs of the AdS radius, that are spinorial generating functions (infinite tower of totally symmetric Majorana spinor-tensor fields of all half-integer spin $s=\frac{1}{2},\frac{3}{2},\dots{},\ensuremath{\infty}$).
Highlights
Among all unconstrained Lagrangian formulations for the higher spin gauge field theory, there exists a simple model describing massless free bosonic higher spin fields in d-dimensional ðAÞdSd spacetime, proposed by Segal in 2001 [1]
In 2018, this formulation was extended to massless free fermionic higher spin fields in d-dimensional ðAÞdSd spacetime [2], which we refer to both as “Segal formulations”.1. These formulations are given by the local and covariant action principles in which there are no constraints on the gauge fields and the gauge parameters, unlike Fronsdal [5,6] and Fang-Fronsdal [7,8] formulations involving some constraints on the gauge fields and parameters, in both Minkowski and anti–de Sitter (AdS) spacetimes
To make clear simplicity of this formalism, let us focus on the Segal action [1] and present some features to compare them with the Fronsdal action [5]: (i) The Fronsdal action describes an arbitrary totally symmetric tensor field Φμ1...μsðxÞ of integer
Summary
Among all unconstrained Lagrangian formulations for the higher spin gauge field theory, there exists a simple model describing massless free bosonic higher spin fields in d-dimensional ðAÞdSd spacetime, proposed by Segal in 2001 [1]. We note that in the framework of superspace formalism the off-shell N 1⁄4 1, d 1⁄4 4 higher superspin massless multiplets were studied first in [14,15], while its generalization to AdS space was given in [16] (see [17,18] for component decomposition) As another application, the present work is devoted to study supersymmetrization of Segal formulation in fourdimensional AdS4. We present our conventions in the appendix A; in appendix B, we review the Wess-Zumino multiplet in AdS4 which includes a manner that we followed to find unconstrained supersymmetry transformations in this work; in appendix C, we illustrate how the SUSY algebra closes on-shell in flat spacetime. Useful relations concerning supersymmetry in AdS and so on will be presented in the appendix D
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