QCD Effective Lagrangian and Condensation of Chromomagnetic Flux Tubes (2509.11375v1)

Abstract: Vacuum polarisation effects induced by the sourceless solutions of the Yang-Mills equation are investigated. These solutions represent oppositely oriented chromomagnetic flux tubes permeating the space in all directions. We review and prove the gauge invariance of the effective Lagrangian on sourceless gauge fields and present a number of alternative methods allowing to compute the effective Lagrangian. We compute the effective Lagrangian on chromomagnetic flux tube solutions and demonstrate that the effective Lagrangian has a universal form that supports the stability of the chromomagnetic flux tubes condensation and indicates that the Yang-Mills vacuum is a highly degenerate state. The stability is a result of the quartic nonlinear self-interaction of the negative mode completely eliminating the instability and the imaginary term from the effective Lagrangian in chromomagnetic field. It is suggested that the condensate of chromomagnetic flux tubes represents a dual analog of the Cooper pairs condensate in a superconductor.