Minimal Supergeometric Quantum Field Theories

TL;DR

This paper develops minimal SuperGeometric Quantum Field Theories that incorporate scalar-fermion transformations with a focus on the geometric structure of the field space, revealing new models with non-zero fermionic curvature.

Contribution

It introduces the first minimal SG-QFT models with non-zero fermionic curvature in both two and four dimensions, clarifying supermetric choices and their effects.

Findings

Different supermetric definitions lead to distinct off-shell theories.

Scalar fields alone cannot induce fermionic curvature beyond scalar contributions.

New models exhibit non-zero fermionic curvature in multiple dimensions.

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.