Abstract
We study the Gluino-Glue operator in the context of Supersymmetric N=1 Yang-Mills (SYM) theory. This composite operator is gauge invariant, and it is directly connected to light bound states of the theory; its renormalization is very important as a necessary step for the study of low-lying bound states via numerical simulations. We make use of a Gauge-Invariant Renormalization Scheme (GIRS). This requires the calculation of the Green's function of a product of two Gluino-Glue operators, situated at distinct space-time points. Within this scheme, the mixing with non-gauge invariant operators which have the same quantum numbers is inconsequential. We compute the one-loop conversion factor relating the GIRS scheme to MS‾. This conversion factor can be used in order to convert to MS‾ Green's functions which are obtained via lattice simulations and are renormalized nonperturbatively in GIRS.
Highlights
The study of Supersymmetric models on the lattice has been very limited to date, due to their sheer complexity
Our work focuses on the supersymmetric Yang-Mills theory with gauge group SU (Nc) and N = 1 supersymmetry generators
In this paper we have studied the Gluino-Glue operator OGg in Supersymmetric Yang-Mills theory (SYM) theory, using variants of a gauge invariant renormalization scheme (GIRS)
Summary
The study of Supersymmetric models on the lattice has been very limited to date, due to their sheer complexity (see e.g. [1,2], and references therein). The conversion factors between an intermediate scheme, such as an RI -like1 [13,14], which is directly applicable in lattice simulations, and MS can be extracted, leading to the determination of a nonperturbative renormalization prescription In such a scheme the calculation of Green’s functions of operators, which are gauge noninvariant and/or depend on ghost fields, is unavoidable. In a recent study [15], we introduced a gauge-invariant renormalization scheme (GIRS), in the spirit of the coordinate space (X-space) scheme [16,17,18,19], which is suitable for renormalizing gauge-invariant operators nonperturbatively, without the issues of ghost terms and gauge fixing This scheme involves Green’s functions of two or more composite operators in different spacetime points, without external elementary fields (see, e.g., Eq (10)).
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