We study the Casimir effect in axion electrodynamics. A finite θ-term affects the energy dispersion relation of photon if θ is time and/or space dependent. We focus on a special case with linearly inhomogeneous θ 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 θ. We call this repulsive component in the Casimir force induced by inhomogeneous θ the anomalous Casimir effect.

Inspired by the duality between gravity and defects in crystals, we study lattice field theory with torsion. The torsion is realized by a line defect of a lattice, namely a dislocation. As the first application, we perform the numerical computation for vector and axial currents induced by a screw dislocation. This current generation is called the chiral torsional effect. We also derive the analytical formula for the chiral torsional effect in the continuum limit.

We scrutinize the novel chiral transport phenomenon driven by spacetime torsion, namely, the chiral torsional effect (CTE). We calculate the torsion-induced chiral currents with finite temperature, density, and curvature in the most general torsional gravity theory. The conclusion complements the previous study on the CTE by including curvature and substantiates the relation between the CTE and the Nieh-Yan anomaly. We also analyze the response of chiral torsional current to an external electromagnetic field. The resulting topological current is analogous to that in the axion electrodynamics.

We study the chiral effective theory in the presence of quantum chromodynamics (QCD) vortices. Gauge invariance requires novel terms from vortex singularities in the gauged Wess-Zumino-Witten action, which incorporate anomaly-induced currents along the vortices. We examine these terms for systems with QCD axial domain-walls bounded by vortices (vortons) under magnetic fields. We discuss how the baryon and electric charge conservations are satisfied in these systems through interplay between domain-walls and vortices, manifesting Callan-Harvey's mechanism of anomaly inflow.

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