Relational Supersymmetry via the Dressing Field Method and Matter-Interaction Supergeometric Framework
arXiv:2503.19077 · doi:10.1002/andp.202500121
Abstract
Relationality is the paradigmatic conceptual core of general-relativistic gauge field theory. It can be made manifest via the Dressing Field Method (DFM) of symmetry reduction, a systematic tool to achieve gauge-invariance by extracting the physical degrees of freedom representing relations among field variables. We review and further expand on some applications of the DFM to the very foundations of the supersymmetric framework, where it allows to build relational supersymmetric field theory and (dis)solves crucial issues. Furthermore, we elaborate on a novel approach within the relational supersymmetric field theory framework giving a unified description of fermionic matter fields and bosonic gauge fields, and thus close to Berezin's original motivation for the introduction of supergeometry in fundamental physics: a Matter-Interaction Supergeometric Unification (MISU). This new approach stands irrespective from the ultimate empirical status of standard supersymmetric field theory, about which it is agnostic.
V2, 28 pages, 2 figures, title updated, version accepted for publication in Annalen der Physik
References in corpus (32)
- Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
- Relational Quantum Mechanics
- Differential Geometry on the Space of Connections via Graphs and Projective Limits
- Generalized Measures in Gauge Theory
- Supersymmetry of a different kind
- Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches
- Artificial vs Substantial Gauge Symmetries: a Criterion and an Application to the Electroweak Model
- Local supersymmetry without SUSY partners
- Gauge invariant composite fields out of connections, with examples
- Connections on Lie algebroids and on derivation-based noncommutative geometry
- On the Configuration Space of Gauge Theorie
- (Anti-)de Sitter, Poincaré, Super symmetries, and the two Dirac points of graphene
- Torsion in quantum field theory through time-loops on Dirac materials
- Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method
- Formulation of gauge theories on transitive Lie algebroids
- Hunting Quantum Gravity with Analogs: the case of graphene
- Unconventional SUSY and Conventional Physics: A Pedagogical Review
- The dressing field method of gauge symmetry reduction, a review with examples
- Nucleon spin decomposition and differential geometry
- Tractors and Twistors from conformal Cartan geometry: a gauge theoretic approach I. Tractors
- Tractors and Twistors from conformal Cartan geometry: a gauge theoretic approach II. Twistors
- Chiral gauge theory and gravity from unconventional supersymmetry
- Residual Weyl symmetry out of conformal geometry and its BRS structure
- Graphene and Black Holes: novel materials to reach the unreachable
- Note on the bundle geometry of field space, variational connections, the dressing field method, & presymplectic structures of gauge theories over bounded regions
- The Quantum Theory of Chern-Simons Supergravity
- Dressing vs. Fixing: On How to Extract and Interpret Gauge-Invariant Content
- BRST structure for the mixed Weyl-diffeomorphism residual symmetry
- Dressing fields for supersymmetry: The cases of the Rarita-Schwinger and gravitino fields
- On the Meaning of Local Symmetries: Epistemic-Ontological Dialectics
- Off-shell supersymmetry via manifest invariance
- Self duality in unconventional conformal supersymmetry