Speaker
Description
Lefschetz thimbles have been discussed recently as a possible solution to the complex action problem (sign problem) in Monte Carlo simulations. Here we discuss the structure of Lefschetz thimbles for pure pure Yang-Mills theories with a complex gauge coupling $\beta$ and show how the gauge degrees of freedom alter the thimble decomposition. We propose to simulate such theories on the union of the tangential manifolds to the thimbles at all critical points. We construct a local Metropolis-type algorithm, that can either be constraint to a specific thimble or simulate across thimbles. However, the more thimbles are included in the simulation, the larger will be the sign problem. We demonstrate the algorithm on a (1+1)-dimensional U(1) model. We also discuss how, starting from the main thimble result, successive sub-leading thimbles can be taken into account via a re-weighting approach.
