Simulating Yang-Mills theories with a complex coupling

Jan M. Pawlowski, Manuel Scherzer, Christian Schmidt, Felix P.G. Ziegler, Felix Ziesché

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Abstrakt

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.

OriginalsprogEngelsk
Artikelnummer094505
TidsskriftPhysical Review D
Vol/bind103
Udgave nummer9
Antal sider18
ISSN2470-0010
DOI
StatusUdgivet - 1. maj 2021

Bibliografisk note

Funding Information:
discussions. C. S. and F. Z. acknowledge support by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Collaborative Research Centre CRC-TR 211 “Strong-interaction matter under extreme conditions” Project No. 315477589 and from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. H2020-MSCAITN-2018-813942 (EuroPLEx). This work is further supported by the ExtreMe Matter Institute EMMI, the Bundesministerium für Bildung und Forschung (BMBF, German Federal Ministry of Education and Research) under Grant No. 05P18VHFCA and by the DFG through the Collaborative Research Centre CRC 1225 (ISOQUANT) as well as by DFG under Germany’s Excellence Strategy EXC-2181/1-390900948 (the Heidelberg Excellence Cluster STRUCTURES). M. S. acknowledges support from DFG under Grant No. STA 283/16-2. F. P. G. Z. acknowledges support by Heidelberg University where a part of this work was carried out. Universität Heidelberg

Funding Information:
The authors thank Andrei Alexandru, Benjamin J?ger, Alexander Lindemeier and Ion-Olimpiu Stamatescu for discussions. C. S. and F. Z. acknowledge support by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Collaborative Research Centre CRC-TR 211 "Strong-interaction matter under extreme conditions" Project No. 315477589 and from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. H2020-MSCAITN-2018-813942 (EuroPLEx). This work is further supported by the ExtreMe Matter Institute EMMI, the Bundesministerium f?r Bildung und Forschung (BMBF, German Federal Ministry of Education and Research) under Grant No. 05P18VHFCA and by the DFG through the Collaborative Research Centre CRC 1225 (ISOQUANT) as well as by DFG under Germany's Excellence Strategy EXC-2181/1-390900948 (the Heidelberg Excellence Cluster STRUCTURES). M. S. acknowledges support from DFG under Grant No. STA 283/16-2. F. P. G. Z. acknowledges support by Heidelberg University where a part of this work was carried out. Universit?t Heidelberg.

Publisher Copyright:
© 2021 American Physical Society. All rights reserved.

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