# Twisted Gauge Fields

## TL;DR

This paper introduces a generalized geometric framework for gauge fields using group action cocycles, extending traditional principal bundle connections and linking to conformal tractors, twistors, and quantum anomalies.

## Contribution

It develops a new class of twisted associated bundles and connections, broadening the geometric understanding of gauge fields beyond standard Yang-Mills theory.

## Key findings

- Generalized gauge fields satisfy the gauge principle but differ from standard fields.
- Conformal tractors and twistors are special cases of the proposed framework.
- The twisted geometry naturally appears in quantum gauge field anomalies.

## Abstract

We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than via mere representations of the structure group. We devise a notion of connection generalising Ehresmann connection on principal bundles, giving rise to the appropriate covariant derivative on sections of these twisted associated bundles (and on twisted tensorial forms). We study the action of the group of vertical automorphisms on the objects introduced (active gauge transformations). We also provide the gluing properties of the local representatives (passive gauge transformations). The latter are generalised gauge fields: They satisfy the gauge principle of physics, but are of a different geometric nature than standard Yang-Mills fields. We also examine the conditions under which this new geometry coexists and mixes with the standard one. We show that (standard) conformal tractors and Penrose's twistors can be seen as simple instances of this general picture. We also indicate that the twisted geometry arises naturally in the definition and study of anomalies in quantum gauge field theory.