Minimal Supergeometric Quantum Field Theories
Abstract
We formulate minimal SuperGeometric Quantum Field Theories (SG-QFTs) that allow for scalar-fermion field transformations in a manifestly reparameterisation covariant manner. First, we discuss the issue of uniqueness in defining the field-space supermetric of the underlying supermanifold, and clarify the fact that different supermetric definitions can lead to distinct theories in the off-shell kinematic region. By adopting natural choices for the field-space supermetric, we~then show that scalar fields alone cannot induce a non-trivial field-space Riemannian curvature in the fermionic sector, beyond the one originating from the scalar part of the theory. We~present for the first time minimal SG-QFT models that feature non-zero fermionic curvature both in two and four spacetime dimensions. Physical applications of SG-QFTs are discussed.
Cite
@article{arxiv.2307.01126,
title = {Minimal Supergeometric Quantum Field Theories},
author = {Viola Gattus and Apostolos Pilaftsis},
journal= {arXiv preprint arXiv:2307.01126},
year = {2023}
}
Comments
17 pages, typos corrected, discussion on the dimensionality of the model parameters added