Abstract
We present a new method of deriving the off-shell spectrum of supergravity and massless 4D, mathcal{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.
Highlights
In many of the above described theories, supersymmetry is a vital ingredient and it is natural to ask for the description of higher spins in the presence of supersymmetry
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 find that for any massless, 4D, N = 1 theory, the supersymmetric auxiliary fields that appear in its off-shell spectrum organise in the following ways: Fermions: There is only one kind of fermionic auxiliary feilds and have the properties (i ) they come in pairs (β, ρ) [L = · · · + β...ρ... + c.c.], (ii ) they are gauge invariant [δgβ... = 0 = δgρ...], (iii )
Summary
Based on the group theoretic analysis of the irreducible representations of the superPoincare group, we know that on-shell they must describe two successive spins, one integer and one half-integer. It is straightforward to count the off-shell degrees of freedom for spin s, the answer is s2 + 2.2 β) For half-integer spin j = s+1/2, we must have three fermionic components ψα(s+1)α (s), ψα(s)α (s−1) and ψα(s−1)α (s−2) with independently symmetrized indices along with gauge transformations δgψα(s+1)α (s) ∼ ∂(αs+1(αs ξα(s))α (s−1)) , δgψα(s)α (s−1) ∼ ∂(αs βξ ̄α(s−1))βα (s−1) , δgψα(s−1)α (s−2) ∼ ∂ββξβα(s−1)βα (s−2). Notice that the off-shell bosonic and fermionic degrees of freedom do not match This is one way to realize that in supersymmetric theories we must introduce extra auxiliary fields in order to balance the bosonic and fermionic d.o.f, as requested by our Supersymmetry requirement
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