Supersymmetric QCD on the Lattice: An Exploratory Study

Abstract

We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric $\mathcal{N}=1$ QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves the Wilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naïve discretization. The gauge group that we consider is $SU(N_c)$, while the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge parameter, $\alpha$, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant ($Z_g$) and of the quark ($Z_{\psi }$), gluon ($Z_u$), gluino ($Z_{\lambda }$), squark ($Z_{A_{\pm }}$), and ghost ($Z_c$) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

arXiv comment19 pages, 10 figures

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• Supersymmetric QCD: Renormalization and Mixing of Composite Operators
• Gauge-invariant Renormalization of the Gluino-Glue operator
• Exploring gauge theories with adjoint matter on the lattice
• Perturbative renormalization of the supercurrent operator in lattice $\mathcal{N}=1$ supersymmetric Yang-Mills theory
• Renormalization and Mixing of the Gluino-Glue Operator on the Lattice
• $\mathcal{N}=1$ Super-Yang-Mills theory on the lattice with twisted mass fermions
• Nonperturbative renormalization of the supercurrent in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory
• Supersymmetric and conformal theories on the lattice: from super Yang-Mills towards super QCD
• Do anomalies break the momentum routing invariance?
• Quark sector effects and glueball mass sensitivity estimates in Lorentz-violating supersymmetric QCD-like theories
• Supercurrent Renormalization in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory