Scalar QED$_2$ with a topological term - a lattice study in a dual representation

We present a dual representation for the partition function of 2-dimensional scalar quantum electrodynamics with a topological term ($\theta$-term). In the dual representation the complex action problem at non-zero $\theta$ is absent, which is an obstacle for Monte Carlo simulations in the conventional form of the model. We discuss the technical aspects of the dual representation and show that a dual Monte Carlo simulation can be implemented. As a first application we demonstrate how the $2\pi$-periodicity of physical observables is recovered in a suitable continuum limit.