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arXiv · 2504.03231

On Spinning Particles, their Partition Functions and Picture Changing Operators

Eugenia Boffo·Pietro Antonio Grassi·Ondřej Hulík·Ivo Sachs
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Abstract

We compute the partition function for the $N=1$ spinning particle, including pictures and the large Hilbert space, and show that it counts the dimension of the BRST cohomology in two- and four-dimensional target space. We also construct a quadratic action in the target space. Furthermore, we find a consistent interaction as a derived bracket based on the associative product of world line fields, leading to an interacting theory of multiforms in space-time. Finally, we comment on the equivalence of the multiform theory with a Dirac fermion. We also identify the chiral anomaly of the latter with a Hodge anomaly for the multiform theory, which manifests itself as a deformation of the gauge fixing.

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Eugenia Boffo, Pietro Antonio Grassi, Ondřej Hulík, Ivo Sachs. 2025-04-04. On Spinning Particles, their Partition Functions and Picture Changing Operators. https://arxiv.org/abs/2504.03231

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