[Paper Review] Simulations of N=1 supersymmetric Yang-Mills theory with three colours

Sajid Ali, Georg Bergner+5 more|arXiv (Cornell University)|Oct 31, 2016

Black Holes and Theoretical Physics7 references4 citations

TL;DR

This paper presents the first numerical simulations of $χ=1$ supersymmetric Yang-Mills theory with SU(3) gauge group and dynamical gluinos using lattice field theory. Employing improved Wilson fermions and Symanzik-improved gauge actions, the study confirms a first-order phase transition in the scalar condensate and observes a single symmetric peak in the gluino condensate distribution, suggesting no spontaneous supersymmetry breaking at the critical hopping parameter $\kappa_c$, though the expected triple-peak structure for $N_c=3$ vacua remains unobserved.

ABSTRACT

We report on our recent results regarding numerical simulations of the four dimensional, N=1 Supersymmetric Yang-Mills theory with SU(3) gauge symmetry and light dynamical gluinos.

Motivation & Objective

• To investigate the non-perturbative dynamics of $χ=1$ supersymmetric Yang-Mills theory with three colours (SU(3)) using lattice field theory.
• To test the recovery of supersymmetry in the continuum limit by tuning the gluino mass to the critical hopping parameter $\kappa_c$.
• To probe the structure of the $N_c=3$ vacua and detect signatures of spontaneous $Z_6$ symmetry breaking via the gluino condensate.
• To measure the low-lying mass spectrum of bound states, including gluinoballs and gluino-glueballs, and assess their supermultiplet degeneracy.
• To estimate discretization effects by simulating at multiple $\beta$ values and extrapolate to the continuum limit.

Proposed method

• Lattice formulation using Wilson fermions in the adjoint representation for gluinos and tree-level Symanzik-improved Wilson gauge action for gluons.
• Application of one to three levels of stout smearing to reduce lattice artifacts in the Wilson-Dirac operator.
• Use of the two-step polynomial hybrid Monte Carlo (TS-PHMC) algorithm for generating gauge configurations, with some results from Rational Hybrid Monte Carlo (RHMC).
• Employment of Ward-Takahashi identities and the adjoint pion mass to determine the critical hopping parameter $\kappa_c$ where the gluino mass vanishes.
• Measurement of the gluino condensate distribution to probe the $Z_6$ vacuum structure and detect possible first-order transitions.
• Extrapolation of bound state masses to the chiral limit by fitting against the square of the adjoint pion mass $m_{\text{a--}\pi}^2$.

Experimental results

Research questions

• RQ1 Does the $\mathcal{N}=1$ SYM theory with SU(3) gauge group exhibit a first-order phase transition in the scalar condensate, as expected from the $Z_6$ vacuum structure?
• RQ2 Is the gluino condensate distribution consistent with the existence of three degenerate vacua at $\kappa_c$, or does it show only a single symmetric peak?
• RQ3 Are the low-lying bound states—such as the $0^{++}$ gluinoball, $0^{-+}$ pseudoscalar, and gluino-glueball—mass-degenerate in the chiral limit, indicating unbroken supersymmetry?
• RQ4 To what extent do discretization effects influence the mass spectrum, and can the continuum limit be reliably extrapolated from $\beta=4.0$ and $\beta=4.3$ simulations?
• RQ5 Does the observed absence of the expected triple-peak structure in the gluino condensate distribution indicate a dynamical suppression of vacuum degeneracy or a lattice artifact?

Key findings

• The critical hopping parameter $\kappa_c$ for $N_c=3$ is determined as $\kappa_c = 0.13860(9)$, where the renormalized gluino mass and the square of the adjoint pion mass both vanish.
• A clear first-order transition is observed in the scalar condensate, indicating spontaneous breaking of the $Z_6$ symmetry.
• The gluino condensate distribution shows only a single symmetric peak at $\kappa_c$, contrary to the expected triple-peak structure for three degenerate vacua.
• The $0^{++}$ channel (gluino-glueball and $f_0$-like state) shows compatible masses in the chiral limit, though with significant noise.
• The $0^{-+}$ and gluino-glueball states exhibit much smaller error bars and their masses are consistent with the $0^{++}$ channel within errors, though not degenerate with each other.
• Discretization effects are suspected to be responsible for the observed mass non-degeneracy between the $0^{-+}$ and $0^{++}$ states, as the results are expected to improve at $\beta=4.3$.