The unphysical nature of the SL(2,R) symmetry and its associated condensates in Yang-Mills theories

TL;DR

This paper uses BRST cohomology to demonstrate that the SL(2,R) symmetry in Yang-Mills theories is unphysical, providing evidence that condensates linked to its breaking lack physical meaning.

Contribution

It offers a cohomological analysis showing the unphysical nature of SL(2,R) symmetry and its condensates in Yang-Mills theories, challenging previous assumptions.

Findings

SL(2,R) symmetry is unphysical in Yang-Mills theories

Condensates associated with SL(2,R) breaking lack physical meaning

Provides a no-go statement for physical interpretation of these condensates

Abstract

BRST cohomology methods are used to explain the origin of the SL(2,R) symmetry in Yang-Mills theories. Clear evidence is provided for the unphysical nature of this symmetry. This is obtained from the analysis of a local functional of mass dimension two and constitutes a no-go statement for giving a physical meaning to condensates associated with the symmetry breaking of SL(2,R).