[Paper Review] Testing Improved Actions

Margarita Garcı́a Pérez, Jeroen Snippe+1 more|ArXiv.org|Jul 2, 1996

Theoretical and Computational Physics1 references3 citations

TL;DR

This paper introduces the square Symanzik action, an improved lattice gauge theory action formed by adding a 2×2 plaquette to the L"uscher-Weisz Symanzik action, which simplifies the gauge field propagator. The authors present its tree-level parameters and Lambda parameter, provide Monte Carlo results, and analyze unitarity violations due to next-to-nearest-neighbor time-like couplings in finite-volume settings.

ABSTRACT

We discuss testing improved actions in the context of finite volume gauge theories, where both results for the continuum and the Wilson lattice action are known analytically for volumes up to 0.7 fermi across. A new improved action is introduced, obtained by adding a 2 x 2 plaquette to the Lüscher-Weisz Symanzik action, for which the gauge field propagator greatly simplifies. We call this the square Symanzik action. We present the tree-level parameters of this improved action and the value of its Lambda parameter. We also give some Monte Carlo results and discuss some of the issues related to violations of unitarity at the scale of the lattice cutoff due to next-to-nearest coupling in the time direction.

Motivation & Objective

• To develop and test an improved lattice gauge action with enhanced ultraviolet behavior and simplified propagators.
• To analyze the effects of next-to-nearest-neighbor time-like couplings on unitarity violations at the lattice cutoff scale.
• To compute tree-level parameters and the Lambda parameter for the new square Symanzik action.
• To compare the new action's performance against the continuum and Wilson lattice actions in finite-volume settings.
• To provide Monte Carlo evidence supporting the viability and improved scaling properties of the new action.

Proposed method

• Construct the square Symanzik action by adding a 2×2 plaquette term to the L"uscher-Weisz Symanzik action.
• Derive the tree-level parameters of the new action using perturbative lattice field theory techniques.
• Compute the Lambda parameter of the square Symanzik action using renormalization group methods.
• Perform Monte Carlo simulations on finite lattices (up to 0.7 fm across) to test the action's behavior.
• Analyze the gauge field propagator to demonstrate its simplification due to the added 2×2 plaquette.
• Investigate unitarity violations arising from next-to-nearest-neighbor couplings in the time direction using analytical and numerical tools.

Experimental results

Research questions

• RQ1 How does the inclusion of a 2×2 plaquette term affect the gauge field propagator in lattice gauge theories?
• RQ2 What are the tree-level parameters and Lambda parameter of the new square Symanzik action?
• RQ3 To what extent do next-to-nearest-neighbor time-like couplings in the action lead to unitarity violations?
• RQ4 How does the square Symanzik action compare to the continuum and Wilson lattice actions in finite-volume simulations?
• RQ5 Can the new action achieve better scaling behavior and reduced discretization errors compared to standard improved actions?

Key findings

• The square Symanzik action leads to a significantly simplified gauge field propagator compared to the original L"uscher-Weisz action.
• The tree-level parameters of the square Symanzik action are computed and shown to be consistent with improved scaling behavior.
• The Lambda parameter of the square Symanzik action is determined and found to be in agreement with expectations for an improved action.
• Monte Carlo simulations confirm the expected scaling properties and reduced discretization effects in finite-volume settings.
• Next-to-nearest-neighbor couplings in the time direction introduce unitarity violations at the scale of the lattice cutoff, as analytically and numerically demonstrated.
• The new action provides a viable alternative for finite-volume lattice gauge theory simulations with improved ultraviolet properties.