Topological Gluon Mass and Shear Viscosity of the Quark--Gluon Plasma

The quark–gluon plasma produced in relativistic heavy–ion collisions behaves as a nearly perfect fluid characterized by an exceptionally small shear viscosity to entropy density ratio. Understanding the microscopic origin of this small viscosity remains an important problem in the theory of strongly interacting matter. In this work we investigate the transport properties of a gluonic plasma in a non–Abelian gauge theory in which gluons acquire a gauge–invariant mass through a topological $B\wedge F$ interaction. Integrating out the antisymmetric tensor field generates an effective massive gluon propagator that modifies the infrared behaviour of gluon exchange processes. Using relativistic kinetic theory and the Boltzmann transport equation we compute the shear viscosity of the plasma and derive the corresponding transport cross section for gluon scattering. The presence of the topological gluon mass provides a natural infrared regulator for $t$–channel gluon exchange, removing the divergence that appears in perturbative QCD with massless gluons. We show that when the topological mass scale is comparable to the soft momentum scale of the plasma, $m\sim gT$, the resulting viscosity to entropy density ratio naturally falls in the range inferred from hydrodynamic analyses of heavy–ion collision experiments. These results suggest that topological mass generation may provide a simple microscopic mechanism contributing to the near–perfect fluidity of the quark–gluon plasma.

💡 Research Summary

The paper addresses the long‑standing puzzle of why the quark‑gluon plasma (QGP) created in relativistic heavy‑ion collisions behaves as an almost perfect fluid with an exceptionally low shear‑viscosity‑to‑entropy‑density ratio η/s, close to the conjectured lower bound 1/4π. In weak‑coupling kinetic‑theory calculations, the shear viscosity grows rapidly as the gauge coupling g becomes small, largely because the dominant t‑channel gluon exchange in elastic gluon‑gluon scattering produces an infrared (IR) divergence. In perturbative QCD this divergence is usually regulated by medium‑induced screening, implemented through Hard Thermal Loop (HTL) resummation, which introduces a Debye mass m_D∼gT.

The authors propose an alternative, gauge‑invariant infrared regulator based on a topological B∧F interaction in a four‑dimensional non‑Abelian SU(N_c) gauge theory. The Lagrangian contains the usual Yang‑Mills term, a kinetic term for an antisymmetric two‑form field B_{\mu\nu}, and a topological coupling (m/4) ε^{\mu\nu\rho\lambda} B_{\mu\nu}F_{\rho\lambda}. Because the action is quadratic in B_{\mu\nu}, the tensor field can be integrated out exactly. The resulting effective action for the gauge field acquires a transverse mass term \