Non-Abelian Tensor Gauge Fields. Enhanced Symmetries

TL;DR

This paper introduces a framework for non-Abelian tensor gauge fields with extended symmetries, constructing gauge-invariant Lagrangians for arbitrary spin fields and demonstrating symmetry enhancement through coupling constant tuning.

Contribution

It defines a new class of extended non-Abelian gauge transformations for tensor fields, allowing gauge-invariant Lagrangians with enhanced symmetries by tuning coupling constants.

Findings

Constructed gauge-invariant quadratic forms for tensor fields.

Demonstrated symmetry enhancement via coupling constant tuning.

Presented explicit free equations for rank-2 and rank-3 gauge fields.

Abstract

We define a group of extended non-Abelian gauge transformations for tensor gauge fields. On this group one can define generalized field strength tensors, which are transforming homogeneously with respect to the extended gauge transformations. The generalized field strength tensors allow to construct two infinite series of gauge invariant quadratic forms. Each term of these infinite series is separately gauge invariant. The invariant Lagrangian is a linear sum of these forms and describes interaction of tensor gauge fields of arbitrarily large integer spins 1,2,.... It does not contain higher derivatives of the tensor gauge fields, and all interactions take place through three- and four-particle exchanges with dimensionless coupling constant. The first term in this sum is the Yang-Mills Lagrangian. The invariance with respect to the extended gauge transformations does not fix the coefficients - the coupling constants - in front of these forms. There is a freedom to vary them without breaking the extended gauge symmetry. We demonstrate that by an appropriate tuning of these coupling constants one can achieve an enhancement of the extended gauge symmetry. This leads to highly symmetric equations. We present the explicit form of the free equations for the rank-2 and rank-3 gauge fields. Their relation to the Schwinger free equation for the rank-3 gauge fields is discussed.