The sign problem and the Lefschetz thimble

Recently, we have proposed a novel approach (arxiv:1205.3996) to deal with the sign problem that hinders Monte Carlo simulations of many quantum field theories (QFTs). The approach consists in formulating the QFT on a Lefschetz thimble. In this paper we concentrate on the application to a scalar field theory with a sign problem. In particular, we review the formulation and the justification of the approach, and we also describe the Aurora Monte Carlo algorithm that we are currently testing.