# Anomalous Casimir effect in axion electrodynamics

## TL;DR

This paper investigates how a spatially varying axion field modifies the Casimir effect, revealing conditions under which the force can become repulsive, termed the anomalous Casimir effect, in axion electrodynamics.

## Contribution

It demonstrates that inhomogeneous axion fields can induce a repulsive component in the Casimir force, a novel effect in axion electrodynamics.

## Key findings

- The Casimir force can be attractive or repulsive depending on the gradient of the axion field.
- Inhomogeneous $ heta$-terms lead to an anomalous, potentially repulsive Casimir effect.
- The effect depends on the spatial variation of the axion field along the $z$-axis.

## Abstract

We study the Casimir effect in axion electrodynamics. A finite $\theta$-term affects the energy dispersion relation of photon if $\theta$ is time and/or space dependent. We focus on a special case with linearly inhomogeneous $\theta$ along the $z$-axis. Then we demonstrate that the Casimir force between two parallel plates perpendicular to the $z$-axis can be either attractive or repulsive, dependent on the gradient of $\theta$. We call this repulsive component in the Casimir force induced by inhomogeneous $\theta$ the anomalous Casimir effect.