Scale Symmetry Breaking from the Dynamics of Maximal Rank Gauge Field Strengths

TL;DR

This paper explores how the dynamics of maximal rank gauge fields can spontaneously break scale invariance, leading to phenomena like mass generation, confining behavior, and potential emergence in various physical theories.

Contribution

It demonstrates that integrating equations of motion for maximal rank gauge fields causes spontaneous scale symmetry breaking across multiple theoretical frameworks.

Findings

Generation of inverse power potentials in particle mechanics

Mass generation in scalar field theories

Confining behavior in gauge theories

Abstract

Scale invariant theories which contain maximal rank gauge field strengths (of $D$ indices in $D$ dimensions) are studied. The integration of the equations of motion of these gauge fields leads to the s.s.b. of scale invariance. The cases in study are: i) the spontaneous generation of $r^{-1}$ potentials in particle mechanics in a theory that contains only $r^{-2}$ potentials in the scale invariant phase, ii) mass generation in scalar field theories iii) generation of non trivial dilaton potentials in generally covariant theories, iv) spontaneous generation of confining behavior in gauge theories. The possible origin of these models is discussed.