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Simulating Yang-Mills theories with a complex coupling

We propose a novel simulation strategy for Yang-Mills theories with a complex coupling, based on the Lefschetz thimble decomposition. We envisage that the approach developed in the present work can also be adapted to QCD at finite density and real-time simulations. Simulations with Lefschetz thimble...

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Bibliographic Details
Main Authors: Pawlowski, Jan M. (Author) , Scherzer, Manuel (Author) , Schmidt, Christian (Author) , Ziegler, Felix P. G. (Author) , Ziesché, Felix (Author)
Format: Article (Journal)
Language:English
Published: 12 May 2021
In: Physical review
Year: 2021, Volume: 103, Issue: 9, Pages: 1-18
ISSN:2470-0029
DOI:10.1103/PhysRevD.103.094505
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1103/PhysRevD.103.094505
Verlag, lizenzpflichtig, Volltext: https://link.aps.org/doi/10.1103/PhysRevD.103.094505
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Author Notes:Jan M. Pawlowski, Manuel Scherzer, Christian Schmidt, Felix P.G. Ziegler, and Felix Ziesché
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Summary:We propose a novel simulation strategy for Yang-Mills theories with a complex coupling, based on the Lefschetz thimble decomposition. We envisage that the approach developed in the present work can also be adapted to QCD at finite density and real-time simulations. Simulations with Lefschetz thimbles offer a potential solution to sign problems in Monte Carlo calculations within many different models with complex actions. We discuss the structure of generalized Lefschetz thimbles for pure Yang-Mills theories with a complex gauge coupling β and show how to incorporate the gauge orbits. We propose to simulate such theories on the union of the tangential manifolds to the relevant Lefschetz thimbles attached to the critical manifolds of the Yang-Mills action. We demonstrate our algorithm on a (1+1)-dimensional U(1) model and discuss how, starting from the main thimble result, successive subleading thimbles can be taken into account via a reweighting approach. While we face a residual sign problem, our novel approach performs exponentially better than the standard reweighting approach.
Item Description:Gesehen am 05.08.2021
Physical Description:Online Resource
ISSN:2470-0029
DOI:10.1103/PhysRevD.103.094505

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