Abstract: 

We introduce a stochastic geometry (Ricci) flow coupled with the stochastic Yang–Mills gauge flow to elucidate the mechanisms underlying quark confinement in quantum chromodynamics (QCD). This framework generates chromo-magnetic and chromo-electric vortices, which drive the area-law behavior — a hallmark of confinement in Yang–Mills theories. Vortices enclosed within Wilson loops induce the area-law asymptotic behavior of vacuum expectation values, while their disappearance, due to topology changes in the hadronic ground state manifold, transitions the system to a perimeter-law regime. Confinement emerges as a consequence of manifold topology changes, mediated by the Aharonov–Bohm effect arising from compact chromo-electric and magnetic fluxes. The stochastic flow naturally accounts for vortex formation and turbulence in the Yang-Mills vacuum, dynamically induced by braiding and knotting of vortices. Furthermore, we derive dimensional transmutation for Yang–Mills fields from the scaling properties of the geometry flow, yielding a relation involving the infrared equilibrium limit of the Planck constant that accurately estimates ΛQCD.

Bio：

Professor Antonino Marciano is a Tenured Full Professor in the Department of Physics at Fudan University. He earned his Ph.D. in Physics in 2008 at the University of Rome. This was followed by Postdoctoral Research Fellowships at the Centre de Physique Théorique in Marseille, a Visiting Fellowship at Princeton University (2011–2012), and a Postdoctoral Fellowship at Dartmouth University (2012–2013), before joining Fudan University in 2014. He has published over 100 research articles in high-impact refereed journals, achieving an H-index of 27 (Google Scholar).