Wilson lines for Rarita-Schwinger field

Question

The Rarita-Schwinger field is a field with a 1-form and a spinor index, $\psi_\mu^a$. It usually has a gauge symmetry $\delta \psi_\mu^a = \partial_\mu \eta^a$ parametrized by an arbitrary spinor $\eta^a$. I want to understand this field more like a gauge field. Does it have holonomy? Can I compute Wilson loops? Surface operators?

Comments

Is $\psi_\mu^a$ a connection in your Lagrangian?

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@Jia Yes I should have called it $A^a_\mu$ or something (: It begins life as a tensor of a 1-form and a spinor, but then it has this gauge transformation that makes it only locally such a thing. It's like a spinor whose components are connections.

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In that case I would imagine yes, since all the items you mentioned quite naturally arise from connections. But I have no clue about the specifics, I wonder if there's "lattice supergravity" study on this.

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I don't understand the situation well, but here are some comments. It would have to be a massless spin 3/2 field to behave as a kind of gauge field - in this case all but two of the components are suppressed by gauge invariance. See, e.g., http://journals.aps.org/prd/abstract/10.1103/PhysRevD.18.3630

Maybe first looking at the gauge description of a massless spin-1/2 field, http://www.sciencedirect.com/science/article/pii/0370269380907406 gives insight into how the fermionic part behaves....