# Why are Majorana fields usually used to introduce gravity in the Rarita-Schwinger Lagrangian?

When first introducing the gravitational interaction for a spin-3/2 Rarita-Schwinger field, Majorana fields are usually used (see for example here at chapter 4, or in Ramond, (6.4.112) ).

Why is this? What are the advantaged of imposing a Majorana condition in this context?

For example, in the Chapter 4 of the DAMTP lectures, the field introduced is a standard spin-3/2 field with one spinor index and one vector index, as required for a gravitino. The gravitino's spin has to be 3/2 because it differs by 1/2 from $j=2$ of the gravitons, and $j=5/2$ is already too much and would require too large gauge invariance.
The minimum $N=1$ supersymmetry is generated by 4 real supercharges which may be imagined to combine to one Weyl (complex chiral) spinor or one Majorana (real non-chiral) spinor. Using the latter approach, the gravitino superpartners of the real graviton by the real supercharges are real, too.
• By the "real one-half of the Dirac spinor", I mean one-half of the degrees of freedom that are present in the Dirac spinor, a spinor with 4 complex components transforming as a spin-1/2 representation of the Lorentz group, and the one-half is obtained by demanding a reality condition so that the 4 complex components become 4 real components. If you understand that the word "Majorana field" in that explanation may mean a field with any $j\in Z+1/2$ and a real condition, then it's just fine, but then I don't understand too well why you don't understand the original text. – Luboš Motl Jan 19 '15 at 17:33