Lefschetz thimbles regularisation of (lattice) field theories was put forward
as a possible solution to the sign problem. Despite elegant and conceptually
simple, it has many subtleties, a major one boiling down to a plain question:
how many thimbles should we take into account? In the original formulation, a
single thimble dominance hypothesis was put forward: in the thermodynamic
limit, universality arguments could support a scenario in which the dominant
thimble (associated to the global minimum of the action) captures the physical
content of the field theory. We know by now many counterexamples and we have
been pursuing multi-thimble simulations ourselves. Still, a single thimble
regularisation would be the real breakthrough. We report on ongoing work aiming
at a single thimble formulation of lattice field theories, in particular
putting forward the proposal of performing Taylor expansions on the dominant
thimble.Comment: 7 pages, 1 figure, Proceedings of the 37th Annual International
Symposium on Lattice Field Theory, 16-22 June 2019, Wuhan, Chin