- Open Access
Unconventional supersymmetry via the dressing field method
Phys. Rev. D 111, 125022 – Published 25 June, 2025
DOI: https://doi.org/10.1103/76n5-4mg1
Abstract
We reconstrue unconventional supersymmetry, a notion introduced by Alvarez-Valenzuela-Zanelli, as an attempt to use the framework of supersymmetric field theory to describe fermionic matter fields and bosonic gauge fields in a unified way, as parts of a single superconnection. It hinges upon the so-called matter ansatz. Unfortunately, the formal and conceptual status of the ansatz has remained unclear, preventing unconventional supersymmetry to be used in a principled way as a general approach beyond the model in which it was first considered. In this paper, we lift this restriction by showing that the ansatz is a special case of the dressing field method, a new systematic tool to exhibit the gauge-invariant content of general-relativistic gauge field theories.
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In the MAG literature, both problems are “solved” (following a construction from the appendix of [68]) by introducing ad hoc the so-called “radius vector” , a -valued 0-form, which is none other than a dressing field for the translation gauge subgroup of the full affine gauge group. So that the basic variable of MAG is the translation-invariant dressed -valued connection, whose dressed -potential part is called the “key relation” of MAG in [69]. Given that the translation gauge group is eliminated via a local ad hoc dressing field, it is an artificial (fake) symmetry, only the (residual) (or ) gauge symmetry is substantive. Thus dressed, MAG therefore simply reproduces standard Cartan geometric treatment of gravity, as will be thoroughly laid out in a forthcoming paper [70]. This further highlights the relevance of the DFM to a diverse range of topics in physics.
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