Table 6.1 Structure of the massless multiplets in D = 4 space-time. In each column we write the multiplicity of fields of spin J contained in the considered multiplet

1 ≤ N ≤ 8 of the supercharges and the available irreducible field representations, named supermultiplets were established. For instance all the massless multiplets in space-time dimensions d = 4 are displayed in Table 6.1.

6.1.3 Supergravity

One point was immediately clear to every one after 1974. Supersymmetry may be global, as in the proposed Wess-Zumino model, but it might also be a candidate local symmetry. In that case all generators of the algebra should generate local symmetries, in particular the translations Pμ. Yet local translations is another word for general coordinate transformations and that means General Relativity. Hence it appeared that a local supersymmetric field theory is necessarily an extension of gravity including also a gauge field for each supercharge Qα . Such a gauge field ψμα appeared to be a spin 32 field. Thus the hunt was open for supergravity, an interacting

Fig. 6.8 The three founders of supergravity in a picture taken in Rome in 2007 at Villa Mondragone on the occasion of the Laurea Honoris Causa to Sergio Ferrara

theory of spin 2 gravitons and spin 32 gravitinos that should be invariant under appropriate local supersymmetry transformations and should reduce to pure Einstein gravity when the gravitinos ψμ are frozen.

For N = 1 the algebraic analysis showed that {2, 32 } corresponds indeed to a massless multiplet in D = 4: hence the conjectured interacting theory was likely to exist and be consistent. In the case of extended supersymmetry, the supergravity Lagrangian had to include all the fields contained in the appropriate graviton multiplet as displayed in Table 6.1. Several researchers addressed the question in different approaches. In 1976 the race was won at the Ecole Normale Superieure of Paris by Daniel Freedman, Sergio Ferrara and Peter van Nieuwenhuizen (see Fig. 6.8), who constructed the Lagrangian of N = 1 supergravity, using a second order formalism [8] and who were later awarded the Dirac Medal for such an achievement. A few week later appeared also a paper [9] by Stanley Deser and Bruno Zumino who ob-