The QCD at finite density is not well understood yet, where standard Monte-Carlo simulation suffers from sign problem. In order to overcome the sign problem, the method of Lefschetz thimble has been explored. Basically, the original sign problem can be less severe in a complexified theory due to the constancy of the imaginary part of an action on each thimble. However, so-called global sign problem which originates from the phase factors assigned on each thimble still remains. This problem may not be negligible in a situation where a large number of thimbles contribute to the partition function.

In [1], we propose a method to resolve the global sign problem by modifying the structure of Lefschetz thimbles so that only a single thimble is relevant to the partition function. It can be shown that observables measured in the original and modified theories are connected by a simple formula. In this talk, we introduce this method and slightly generalize our previous work. We exemplify that our method works in toy models.

[1] S. Tsutsui and T. M. Doi, Phys. Rev. D94, 074009 (2016)

Theoretical Developments