Lattice QCD on Non-Orientable Manifolds

Abstract

A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge, when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the connectivity of the configuration space is changed. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance strongly. Here we propose to use a non-orientable manifold, and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is, that translational invariance is preserved up to exponentially small corrections. A Dirac-fermion on a non-orientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to circumvent this problem.

9 pages, 8 figures; v2: matches accepted version

References in corpus (8)

• High-precision scale setting in lattice QCD
• Critical slowing down and error analysis in lattice QCD simulations
• Finite volume QCD at fixed topological charge
• Topological susceptibility at high temperature on the lattice
• Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
• $S$-duality of $u(1)$ gauge theory with $\theta =\pi$ on non-orientable manifolds: Applications to topological insulators and superconductors
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Cited by in corpus (14)

• FLAG Review 2019
• FLAG Review 2021
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• The topological susceptibility in finite temperature QCD and axion cosmology
• FLAG Review 2024
• Lattice QCD for Cosmology
• Topological critical slowing down: variations on a toy model
• Proof of the renormalizability of the gradient flow
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• Ergodic sampling of the topological charge using the density of states
• Interpreting Numerical Measurements in Fixed Topological Sectors
• Scaling properties of multiscale equilibration
• Hadron Physics from Lattice QCD
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling