The impact of the finite-size effects on the vacuum free energy density of full QCD with $N_f$ massless flavors in the presence of a homogeneous (anti-)self-dual Abelian background gluon field is studied. The zero-temperature free energy density of the four-dimensional spherical domain is computed as a function of the background field strength $B$ and domain radius $R$. The calculation is performed in the one-loop approximation improved by accounting for mixing of the quark and gluon quasizero modes with normal modes, with the use of the $\zeta$-function regularization. It is indicated that, under plausible assumptions on the character of the mixing, the quantum correction to the free energy density has a minimum as a function of $B$ and $R$. Within the mean-field approach to the QCD vacuum based on the domain wall network representation of the mean field, the existence of the minimum may prevent infinite growth of individual domains, thus protecting the vacuum from the long-range ordering, and hence serving as the origin of disorder in the statistical ensemble of domain wall networks, driven by the minimization of the overall free energy of the dominant gauge field configurations.

• Received 16 December 2020
• Accepted 1 June 2021

DOI:https://doi.org/10.1103/PhysRevD.103.114021

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Published by the American Physical Society