Massless fermionic current of Schwinger pairs in 3D de Sitter spacetime

Abstract

Pair creation from the vacuum in the presence of a U(1) gauge field in de Sitter $(\mathrm{dS})$ spacetime provides an important setting for exploring quantum field theory in curved backgrounds. In this work, we investigate massless fermion production and the associated induced current generated by a constant electric field in (1+2)-dimensional $\mathrm{dS}$ spacetime. Assuming the Bunch--Davies vacuum and employing adiabatic regularization, we derive, for the first time, a finite expression for the induced current of massless fermions in $\mathrm{dS}_{3}$. The produced fermions generate a net current opposite to the external electric field. In the strong-field regime, the induced current exhibits the expected semiclassical scaling and reproduces the standard Schwinger behavior in the flat-spacetime limit. In the weak-field regime, the current is linear in the electric-field strength. This behavior is characteristic of the fermionic nature of the particles, since the corresponding bosonic case exhibits infrared hyperconductivity, which is absent in our study. We further show that the induced current remains monotonic throughout the parameter space and, unlike in $\mathrm{dS}_4$, does not exhibit any sign change. Our results thus highlight the role of dimensionality and clarify the interplay between spin and infrared physics in $\mathrm{dS}$. This work provides a consistent basis for future investigations including backreaction effects, topologically massive fermions, and time-dependent electromagnetic backgrounds.