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Casimir effect in Yang-Mills theories in three and four dimensions

Dimitra Karabali1,3,*, Antonina Maj3,†, and V. P. Nair2,3,‡

  • *Contact author: dimitra.karabali@lehman.cuny.edu
  • †Contact author: amaj@gradcenter.cuny.edu
  • ‡Contact author: vpnair@ccny.cuny.edu
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Phys. Rev. D 112, 094037 – Published 19 November, 2025

DOI: https://doi.org/10.1103/7cfj-4b6t

Abstract

We calculate the Casimir energy for the configuration of two parallel plates coupled to non-Abelian gauge fields with a Yang-Mills action. We consider both 2+1 and 3+1 dimensions in the manifestly gauge-invariant formalism we have pursued over the last several years which allows us to factor out the gauge degrees of freedom. A boundary action in the functional integral, equivalent to the insertion of operators representing the plates, is used to enforce the required boundary conditions for the gauge fields. The result is for a kinematic regime corresponding to the exchange of gluons with a dynamically generated mass. We find good agreement in 2+1 dimensions and reasonable agreement in 3+1 dimensions with lattice-based numerical evaluations.

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Phys. Rev. D 112, 094037– Published 19 November, 2025
  • Received 17 September 2025
  • Accepted 29 October 2025
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