From Diophantus to supergravity and massless higher spin multiplets

Abstract

We present a new method of deriving the off-shell spectrum of supergravity and massless 4D, N = 1 higher spin multiplets without the need of an action and based on a set of natural requirements: (a.) existence of an underlying superspace description, (b.) an economical description of free, massless, higher spins and (c.) equal numbers of bosonic and fermionic degrees of freedom. We prove that for any theory that respects the above, the fermionic auxiliary components come in pairs and are gauge invariant and there are two types of bosonic auxiliary components. Type (1) are pairs of a (2, 0)-tensor with real or imaginary (1, 1)-tensor with non-trivial gauge transformations. Type (2) are singlets and gauge invariant. The outcome is a set of Diophantine equations, the solutions of which determine the off-shell spectrum of supergravity and massless higher spin multiplets. This approach provides (i ) a classification of the irreducible, supersymmetric, representations of arbitrary spin and (ii ) a very clean and intuitive explanation to why some of these theories have more than one formulations (e.g. the supergravity multiplet) and others do not.

Higher spin supersymmetry at the cosmological collider: sculpting SUSY rilles in the CMB

“…the construction of fermionic D-brane actions is accomplished by relying on the underlying supersymmetry of the theory [95][96][97][98]. Guided by this, and building on recent developments in the construction of supersymmetric higher spin theories [23][24][25][26][27][28][29][30][31][32][34][35][36][37], we have studied the imprint of higher spin supersymmetry at the cosmological collider.…”

“…In this work we consider a tripartite marriage of 4D, N = 1 supersymmetric higher spins [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] with the effective field theory (EFT) of inflation [38] and de Sitter supergravity [39][40][41]. We construct an effective field theory of a supersymmetric theory of higher spins in a quasi-de Sitter spacetime with spontaneously broken supersymmetry and spontaneously broken time-translation invariance.…”

“…This approach has been further explored in [26][27][28][29]. Later studies of free supersymmetric, massless higher spin supermultiplets include [30][31][32][33].…”

Integer superspin supercurrents of matter supermultiplets

“…This approach has been further explored in [32][33][34][35]. Later studies of free supersymmetric, massless higher spin supermultiplets include [36][37][38].…”

Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions

“…The massless, higher spin irreducible representations of the 4D, N = 1, super-Poincaré were first described in [51] using a component Lagrangian invariant under on-shell supersymmetry. Later a superfield formulation was introduced in [52][53][54] (see also [56][57][58]). A synopsis of the description of higher spin supermultiplets is the following:…”