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Shear and bulk viscosity for a pure glue theory using an effective matrix model

Manas Debnath1,*, Ritesh Ghosh2,†, Najmul Haque1,‡, Yoshimasa Hidaka3,4,§, and Robert D. Pisarski5,∥

  • *Contact author: manas.debnath@niser.ac.in
  • †Contact author: Ritesh.Ghosh@asu.edu
  • ‡Contact author: nhaque@niser.ac.in
  • §Contact author: yoshimasa.hidaka@yukawa.kyoto-u.ac.jp
  • ∥Contact author: pisarski@bnl.gov
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Phys. Rev. D 112, 014040 – Published 28 July, 2025

DOI: https://doi.org/10.1103/y9pd-lpv7

Abstract

At nonzero temperatures, the deconfining phase transition can be analyzed using an effective matrix model to characterize the change in holonomy. The model includes gluons and two-dimensional ghost fields in the adjoint representation, or “teens.” As ghosts, the teen fields are responsible for the decrease of the pressure as T→Td, with Td the transition temperature for deconfinement. Using the solution of this matrix model for a large number of colors, the parameters of the teen fields are adjusted so that the expectation value of the Polyakov loop is close to the values from the lattice. The shear, η, and bulk, ζ, viscosities are computed at nonzero holonomy to leading logarithmic order in weak coupling. In the pure glue theory, the value of the Polyakov loop is relatively large in the deconfined phase, ≈1/2 at Td. Consequently, if s is the entropy density, while η/s decreases as T→Td, it is still well above the conformal bound. In contrast, ζ/s is largest at Td, comparable to η/s, then falls off rapidly with increasing temperature and is negligible by ∼2Td.

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Phys. Rev. D 112, 014040– Published 28 July, 2025
  • Received 7 May 2025
  • Accepted 26 June 2025
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