[Paper Review] One loop calculation of SUSY Ward-Takahashi identity on lattice with Wilson fermion

Yusuke Taniguchi|arXiv (Cornell University)|Jun 24, 1999

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This paper performs a one-loop calculation of the SUSY Ward-Takahashi identity in lattice super Yang-Mills theory using Wilson fermions, demonstrating that the additive mass correction from the SUSY identity matches that from axial U(1)_R symmetry, as predicted by Curci and Veneziano. It shows that both supersymmetry and axial U(1)_R symmetry can be recovered in the continuum limit through a single fine-tuning of parameters, resolving lattice artifacts and identifying operator mixing of the supercurrent with a gauge-invariant current related to the gamma-trace anomaly.

ABSTRACT

One loop correction to the SUSY Ward-Takahashi identity is calculated on lattice with Wilson fermion. The supersymmetry on lattice is broken explicitly by the gluino mass and the lattice artifact. We should fine tune parameters in the theory to the point given by the additive mass correction in order to eliminate the breaking effect of lattice artifact. It is shown that the additive mass correction appearing from the SUSY Ward-Takahashi identity coincide with that from the axial $U(1)_R$ symmetry as was suggested by Curci and Veneziano. Two important symmetries of the super Yang-Mills theory can be recovered simultaneously in the continuum with a single fine tuning. Operator mixing of the supercurrent are also investigated. We find that the supercurrent mixes only with a gauge invariant current $T_μ$ which is related to the gamma-trace anomaly.

Motivation & Objective

• To investigate the one-loop quantum corrections to the SUSY Ward-Takahashi identity in lattice super Yang-Mills theory with Wilson fermions.
• To determine whether the additive mass correction from the SUSY identity matches that from axial U(1)_R symmetry, as suggested by Curci and Veneziano.
• To examine operator mixing of the supercurrent in the presence of lattice artifacts and explicit symmetry breaking.
• To assess whether both supersymmetry and axial U(1)_R symmetry can be simultaneously restored in the continuum limit with a single fine-tuning of parameters.

Proposed method

• One-loop perturbative calculation of the SUSY Ward-Takahashi identity is performed on the lattice using Wilson fermions.
• The additive mass correction is extracted from the SUSY Ward-Takahashi identity and compared with the correction from axial U(1)_R symmetry.
• The supercurrent is analyzed for mixing with other currents, particularly a gauge-invariant current T_μ related to the gamma-trace anomaly.
• The analysis includes the treatment of lattice artifacts and explicit breaking due to the gluino mass and Wilson term.
• Fine-tuning of parameters is applied to cancel the additive mass corrections and restore continuum symmetries.
• The consistency of the results with Curci and Veneziano's conjecture is evaluated through explicit comparison of mass corrections.

Experimental results

Research questions

• RQ1 Does the additive mass correction derived from the SUSY Ward-Takahashi identity coincide with that from axial U(1)_R symmetry in the lattice formulation with Wilson fermions?
• RQ2 Can both supersymmetry and axial U(1)_R symmetry be restored in the continuum limit through a single fine-tuning of parameters?
• RQ3 What is the nature of operator mixing for the supercurrent in the lattice formulation with Wilson fermions?
• RQ4 How do lattice artifacts and explicit breaking terms affect the structure of the SUSY Ward-Takahashi identity at one loop?
• RQ5 Is the current T_μ, related to the gamma-trace anomaly, the only gauge-invariant current that mixes with the supercurrent?

Key findings

• The additive mass correction obtained from the SUSY Ward-Takahashi identity exactly matches the correction from axial U(1)_R symmetry, confirming the conjecture by Curci and Veneziano.
• Both supersymmetry and axial U(1)_R symmetry can be simultaneously restored in the continuum limit with a single fine-tuning of the gluino mass and lattice parameters.
• The supercurrent mixes exclusively with a gauge-invariant current T_μ, which is linked to the gamma-trace anomaly in the theory.
• The lattice artifacts and explicit breaking from the Wilson term are shown to contribute to the additive mass correction, requiring fine-tuning to restore symmetry.
• The one-loop calculation confirms that the structure of the supercurrent and its mixing are consistent with the known anomalies and symmetry constraints in super Yang-Mills theory.