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Non-Abelian Casimir effect for plates, symmetrical tube, and box on the lattice

B. A. Ngwenya1,2,*, A. Rothkopf2,3,†, and W. A. Horowitz1,4,5,‡

  • 1Department of Physics, University of Cape Town Private Bag X3, Rondebosch 7701, South Africa
  • 2Faculty of Science and Technology, University of Stavanger 4021 Stavanger, Norway
  • 3Department of Physics, Korea University, Seoul 02841, Republic of Korea
  • 4Department of Physics, New Mexico State University, Las Cruces, New Mexico, 88003, USA
  • 5Theoretical Sciences Visiting Program, Okinawa Institute of Science and Technology Graduate University, Onna, 904-0495, Japan

  • *Contact author: ngwble001@myuct.ac.za
  • †Contact author: akrothkopf@korea.ac.kr
  • ‡Contact author: wa.horowitz@uct.ac.za
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Phys. Rev. D 114, 014512 – Published 17 July, 2026

DOI: https://doi.org/10.1103/22p4-bxhs

Abstract

We present nonperturbative results of the Casimir potential in non-Abelian SU(3) gauge theory in (2+1)D and (3+1)D in the confined and deconfined phase. For the first time, geometries beyond parallel plates in (3+1)D are explored and we show that the Casimir effect for the symmetrical tube and symmetrical box is attractive. The Casimir potential for the tube differs from the massless noninteracting scalar field theory prediction, where a repulsive Casimir potential is expected. Unlike the parallel plate geometry where the plate size is fixed, in the case of the tube and box, the sizes of the faces forming the walls of the geometries changes with separation distance. We propose various methods that can be used to account for the energy contributions from creating the boundaries. We show that increasing the temperature from a confined to a deconfined phase does not alter the Casimir potential. This observation is consistent with prior work suggesting that the region inside the walls is a boundary induced deconfined phase.

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Phys. Rev. D 114, 014512– Published 17 July, 2026
  • Received 1 October 2025
  • Accepted 2 June 2026
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