Extended Gauge Theories in Euclidean Space with Higher Spin Fields

TL;DR

This paper explores the quantum properties and extensions of an extended Euclidean gauge theory with higher spin fields, including supersymmetric and matter couplings, demonstrating its renormalizability and symmetry breaking features.

Contribution

It introduces new generalizations of the extended gauge theory, including matter fields, supersymmetry, and internal symmetries, and analyzes their quantum aspects and symmetry breaking.

Findings

The pure gauge model is quantized in covariant gauges.

Matter fermions in the adjoint representation are incorporated, with maximum spin 3/2.

Extensions include supersymmetry and internal gauge symmetries, with analysis of spontaneous symmetry breaking.

Abstract

The extended Yang-Mills gauge theory in Euclidean space is a renormalizable (by power counting) gauge theory describing a local interacting theory of scalar, vector, and tensor gauge fields (with maximum spin 2). In this article we study the quantum aspects and various generalizations of this model in Euclidean space. In particular the quantization of the pure gauge model in a common class of covariant gauges is performed. We generalize the pure gauge sector by including matter fermions in the adjoint representation of the gauge group and analyze its N=1 and N=2 supersymmetric extensions. We show that the maximum half-integer spin contained in these fermion fields in dimension 4 is 3/2. Moreover we develop an extension of this theory so as to include internal gauge symmetries and the coupling to bosonic matter fields. The spontaneous symmetry breaking of the extended gauge symmetry is also analyzed.