Kaluza-Klein Schwinger effect

We show that electric fields in compactified spaces may produce Kaluza-Klein (KK) particles even when the energy of electric fields is smaller than KK scale. As an illustrating example, we consider a charged massless complex scalar coupled to U(1) gauge theory in $\mathbb{R}^{1,3}\times {\mathbb S}^1$ and discuss the effect of background gauge potential along a compact direction. The electric field produces the charged Kaluza-Klein particle non-perturbatively, which we call KK Schwinger effect. We quantitatively show that KK modes can be produced even when the electric field energy is much below the KK scale. The mechanism is rather general and similar phenomena would occur in any compactification models when a gauge potential along compact direction evolves in time and experiences large enough field excursion. We also discuss the subtlety of four dimensional effective theory truncated by KK modes at an initial time, when the electric field is turned on.