Topological Casimir effect in Maxwell Electrodynamics on a Compact Manifold

TL;DR

This paper investigates the topological Casimir effect in Maxwell theory on a compact manifold, highlighting its unique sensitivity to external magnetic fields and its distinction from the conventional Casimir effect.

Contribution

It provides a calculation of the topological term in quantum Maxwell theory on a compact manifold and discusses its potential experimental detectability via magnetic field sensitivity.

Findings

Topological Casimir effect is much smaller than the conventional effect.

It is highly sensitive to external magnetic fields.

External magnetic field acts like a $ heta$ parameter, similar to QCD and topological insulators.

Abstract

We study the Topological Casimir effect, in which extra vacuum energy emerges as a result of the topological features of the theory, rather than due to the conventional fluctuations of the physical propagating degrees of freedom. We compute the corresponding topological term in quantum Maxwell theory defined on a compact manifold. Numerically, the topological effect is much smaller than the conventional Casimir effect. However, we argue that the Topological Casimir Effect is highly sensitive to an external magnetic field, which may help to discriminate it from the conventional Casimir effect. It is quite amazing that the external magnetic field plays the role of the $\theta$ state, similar to a $\theta$ vacuum in QCD, or $\theta=\pi$ in topological insulators.