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Taking up superspace- What would it take to be a realist about superspace?

Abstract Modern supersymmetric theories present an interesting interpretative challenge. As a result of consistency conditions on the algebra of the supersymmetry (SUSY) generators, one is led to the idea that SUSY, although traditionally defined as a dynamical symmetry between bosons and fermions, could also be thought of as a spacetime symmetry in some extended spacetime, known as superspace. Supersymmetry is, among other things, a crucial part of the string theoretic framework for a theory of quantum gravity. This paper focuses on what it would take to argue for an interpretation that favours the superspace formulation. After setting up the relevant terminology and distinctions, I introduce a stripped down toy model of a supersymmetric field theory and argue for a special case of a more general thesis--- that one needs some pre-existing philosophical commitment to favour one mathematical formulation over another. I then consider three extant arguments from the literature on the philosophy of spacetime as candidates for such a position in the context of supersymmetric theories.Author Information:

Tushar Menon

Philosophy

University of Oxford