格点场论的顶针正则化：它只是一个梦吗？
One-thimble regularisation of lattice field theories: is it only a dream?
摘要：
Lefschetz顶针正则化（格）场论被提出作为一个可能的解决方案的符号问题。尽管它优雅而概念简单，但它有许多微妙之处，其中一个主要问题归结为一个简单的问题：我们应该考虑多少顶针？在最初的表述中，提出了一个单一的顶针优势假说：在热力学极限中，普适性论证可以支持这样一种情景，即主导顶针（与作用的全局最小值相关）捕获了场论的物理内容。到目前为止，我们已经知道了许多反例，我们自己也一直在进行多顶针模拟。尽管如此，一个顶针正规化将是真正的突破。我们报告正在进行的工作，针对一个单一的顶针制定的晶格场论，特别是提出了建议，执行泰勒展开的主导顶针。
英文摘要：
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.
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