Casimir Force in Spacetimes with Torsion

Abstract

We compute the Casimir force between perfectly conducting parallel plates in a spacetime endowed with constant axial torsion. Working within an effective field theory framework where torsion couples to the electromagnetic sector via a gauge-invariant Chern--Simons-type interaction, we derive the modified photon dispersion relation and mode spectrum. Using zeta-function regularization, we obtain the vacuum energy and the resulting Casimir pressure to second order in the torsion parameter. Our calculation yields a correction scaling as $\Delta P/P_0 = -\frac{5\xi^2 S_z^2 a^2}{4\pi^2} + \order(S_z^4)$, which corresponds to a slight weakening of the attractive Casimir force. We acknowledge a known subtlety in the literature: because the Chern-Simons interaction is a total derivative, some analyses conclude that it should not contribute to the Casimir energy for standard boundary conditions, implying the leading correction is of higher order, $\order(S_z^4)$. For experimentally accessible plate separations ($a \sim \qty{1}{\micro\meter}$), the effect remains well below current detection thresholds ($|\Delta P/P_0| \lesssim 10^{-30}$) due to stringent bounds on macroscopic torsion from spin-torsion coupling experiments. Nevertheless, the calculation establishes a consistent, gauge-invariant bridge between quantum vacuum phenomena and non-Riemannian geometry. We discuss finite-temperature effects and geometric asymmetries as potential pathways for enhancing sensitivity, while placing the results in the broader context of dynamical torsion, condensed matter analogs, and quantum information protocols. Our results are consistent with the CPT-odd photon sector of the Standard-Model Extension and provide a geometric interpretation of Lorentz-violating coefficients in terms of spacetime torsion.