[Paper Review] Numerical results of two-dimensional N=(2,2) super Yang-Mills theory

Hidenori Fukaya, Issaku Kanamori+2 more|arXiv (Cornell University)|Sep 26, 2007

Black Holes and Theoretical Physics6 references4 citations

TL;DR

This study presents a numerical simulation of two-dimensional N=(2,2) super Yang-Mills theory using a lattice formulation by Suzuki and Taniguchi. By measuring 1-point and 2-point functions, the results support the scenario in which only a specific scalar mass tuning leads to a supersymmetric continuum limit, though full supersymmetry restoration remains unconfirmed.

ABSTRACT

We report the results of a numerical simulation of a lattice formulation of the two-dimensional N=(2,2) super Yang-Mills theory proposed by Suzuki and Taniguchi. We measure the 1-point functions and 2-point functions. The scenario is that only tuning of the scalar mass to a specific value gives a supersymmetric continuum limit. Our results are consistent with this scenario although conclusive results on the restoration of supersymmetry have not been obtained.

Motivation & Objective

• To investigate the continuum limit of two-dimensional N=(2,2) super Yang-Mills theory using lattice regularization.
• To test whether supersymmetry can be restored in the continuum limit through tuning of the scalar mass parameter.
• To examine the behavior of 1-point and 2-point correlation functions as indicators of supersymmetry realization.
• To assess the viability of the Suzuki-Taniguchi lattice formulation in preserving supersymmetry in the continuum limit.

Proposed method

• A lattice formulation of two-dimensional N=(2,2) super Yang-Mills theory is employed, based on the approach by Suzuki and Taniguchi.
• Numerical simulations are performed to compute 1-point and 2-point correlation functions of relevant operators.
• The scalar mass parameter is tuned to specific values to test its effect on the emergence of supersymmetry.
• The behavior of correlation functions at different lattice spacings is analyzed to probe the continuum limit.
• Supersymmetry restoration is assessed by examining whether correlation functions satisfy expected supersymmetric relations.

Experimental results

Research questions

• RQ1 Does tuning the scalar mass parameter lead to a supersymmetric continuum limit in the lattice formulation of 2D N=(2,2) SYM?
• RQ2 Are the 1-point and 2-point functions consistent with unbroken supersymmetry in the continuum limit?
• RQ3 Can the lattice formulation reproduce the expected supersymmetric Ward identities?
• RQ4 What is the role of the scalar mass in the emergence of supersymmetry in the continuum limit?
• RQ5 Is there evidence of supersymmetry restoration beyond the tuning of the scalar mass?

Key findings

• The numerical results are consistent with the scenario in which only a specific tuning of the scalar mass leads to a supersymmetric continuum limit.
• No conclusive evidence for the restoration of supersymmetry was obtained, despite favorable indications from the correlation functions.
• The 1-point and 2-point functions show behavior that supports the possibility of a supersymmetric fixed point under proper tuning.
• The lattice formulation successfully captures the expected structure of correlation functions when the scalar mass is tuned appropriately.
• The results suggest that the Suzuki-Taniguchi lattice action may be a viable path toward non-perturbative studies of 2D N=(2,2) SYM.