Abstract
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.
Highlights
In order to test the Standard Model and search for new physics in experiments involving hadrons and nuclei, precision calculations of Standard Model observables are required
Lattice quantum chromodynamics (QCD) calculations using Monte Carlo (MC) methods are performed in Euclidean spacetime where the action SðUÞ is typically a real function of the discretized gauge field Ux;μ ∈ SUð3Þ and an ensemble of gauge fields can be generated with probability distribution proportional to e−SðUÞ
We review the deformed observable approach presented in Ref. [48], in which contour deformations of lattice field theory path integrals are used to define modified observables with improved noise properties and unchanged expectation value
Summary
In order to test the Standard Model and search for new physics in experiments involving hadrons and nuclei, precision calculations of Standard Model observables are required. This paper introduces a simple yet expressive family of complexified manifolds for taming sign/StN problems in SUðNÞ gauge theory using path integral contour deformations. The Jacobians required for calculations using this family of deformations are shown to be triangular matrices whose determinants can be computed with a cost that scales linearly with the spacetime volume This family of manifolds can be applied to all theories involving SUðNÞ gauge fields, including gauge theories coupled to matter fields, their practical utility for improving sign/StN problems is only explored here for pure gauge theory.
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