Supergeometric Quantum Effective Action

TL;DR

This paper develops a novel framework for supergeometric quantum field theories, calculating the one-loop effective action with non-zero fermionic curvature, revealing diffeomorphism-invariant EFT operators and outlining higher-loop extensions.

Contribution

It introduces a new approach to compute the supergeometric quantum effective action, including a generalized Clifford algebra and heat-kernel technique, extending previous theories beyond standard supersymmetry.

Findings

Derived the one-loop effective action for minimal SG-QFTs with fermionic curvature.

Identified diffeomorphism-invariant EFT operators up to four derivatives.

Outlined the extension to higher-loop calculations.

Abstract

Supergeometric Quantum Field Theories (SG-QFTs) are theories that go beyond the standard supersymmetric framework, since they allow for general scalar-fermion field transformations on the configuration space of a supermanifold, without requiring an equality between bosonic and fermionic degrees of freedom. After revisiting previous considerations, we extend them by calculating the one-loop effective action of minimal SG-QFTs that feature non-zero fermionic curvature in two and four spacetime dimensions. By employing an intuitive approach to the Schwinger-DeWitt heat-kernel technique and a novel field-space generalised Clifford algebra, we derive the ultra-violet structure of characteristic effective-field-theory (EFT) operators up to four spacetime derivatives that emerge at the one-loop order and are of physical interest. Upon minimising the impact of potential ambiguities due to the so-called multiplicative anomalies, we find that the EFT interactions resulting from the one-loop supergeometric effective action are manifestly diffeomorphically invariant in configuration space. The extension of our approach to evaluating higher-loops of the supergeometric quantum effective action is described. The emerging landscape of theoretical and phenomenological directions for further research of SG-QFTs is discussed.