Scalar Field in Any Dimension from the Higher Spin Gauge Theory Perspective

TL;DR

This paper reformulates the scalar field equations in arbitrary dimensions using higher spin covariant conditions, providing a new perspective that unifies flat and AdS spaces and explores interactions with auxiliary fields.

Contribution

It introduces a higher-spin covariant framework for scalar fields in any dimension, extending the action principle to include auxiliary fields and interactions.

Findings

Reformulation of scalar field equations as higher spin covariant conditions

Equivalent action to Klein-Gordon at free level, differing at interaction level

Analysis of Yang-Mills current interactions in AdS space

Abstract

We formulate the equations of motion of a free scalar field in the flat and $AdS$ space of an arbitrary dimension in the form of some "higher spin" covariant constancy conditions. Klein-Gordon equation is interpreted as a non-trivial cohomology of a certain "\sgm-complex". The action principle for a scalar field is formulated in terms of the "higher-spin" covariant derivatives for an arbitrary mass in $AdS_d$ and for a non-zero mass in the flat space. The constructed action is shown to be equivalent to the standard first-order Klein-Gordon action at the quadratic level but becomes different at the interaction level because of the presence of an infinite set of auxiliary fields which do not contribute at the free level. The example of Yang-Mills current interaction is considered in some detail. It is shown in particular how the proposed action generates the pseudolocally exact form of the matter currents in $AdS_d$.