Path integral contour deformations for observables in SU(N) gauge theory

William Detmold (Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA; The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, Cambridge, Massachusetts 02139, USA) ; Gurtej Kanwar (Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA; The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, Cambridge, Massachusetts 02139, USA) ; Henry Lamm (Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA) ; Michael L. Wagman (Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA) ; Neill C. Warrington (Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195-1550)

Path integral contour deformations have been shown to mitigate sign and signal-to-noise problems associated with phase fluctuations in lattice field theories. We define a family of contour deformations applicable to SU(N) lattice gauge theory that can reduce sign and signal-to-noise problems associated with complex actions and complex observables. For observables, these contours can be used to define deformed observables with identical expectation value but different variance. As a proof-of-principle, we apply machine learning techniques to optimize the deformed observables associated with Wilson loops in two dimensional SU(2) and SU(3) gauge theory. We study loops consisting of up to 64 plaquettes and achieve variance reduction of up to 4 orders of magnitude.

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      "title": "Path integral contour deformations for observables in <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> gauge theory"
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  "abstracts": [
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      "source": "APS", 
      "value": "Path integral contour deformations have been shown to mitigate sign and signal-to-noise problems associated with phase fluctuations in lattice field theories. We define a family of contour deformations applicable to <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> lattice gauge theory that can reduce sign and signal-to-noise problems associated with complex actions and complex observables. For observables, these contours can be used to define deformed observables with identical expectation value but different variance. As a proof-of-principle, we apply machine learning techniques to optimize the deformed observables associated with Wilson loops in two dimensional <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> and <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> gauge theory. We study loops consisting of up to 64 plaquettes and achieve variance reduction of up to 4 orders of magnitude."
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Published on:
24 May 2021
Publisher:
APS
Published in:
Physical Review D , Volume 103 (2021)
Issue 9
DOI:
https://doi.org/10.1103/PhysRevD.103.094517
arXiv:
2101.12668
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: