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Renormalization and Mixing of the Gluino-Glue Operator on the Lattice
High Energy Physics - Lattice · Submitted 6 Oct 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We calculate its renormalization, which is not only multiplicative, due to the fact that this operator can mix with non-gauge invariant operators of equal or, on the lattice, lower dimension.
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We study the mixing of the Gluino-Glue operator in ${\cal N}$=1 Supersymmetric Yang-Mills theory (SYM), both in dimensional regularization and on the lattice. We calculate its renormalization, which is not only multiplicative, due to the fact that this operator can mix with non-gauge invariant operators of equal or, on the lattice, lower dimension. These operators carry the same quantum numbers under Lorentz transformations and global gauge transformations, and they have the same ghost number. We compute the one-loop quantum correction for the relevant two-point and three-point Green's functions of the Gluino-Glue operator. This allows us to determine renormalization factors of the operator in the $\overline{\textrm{MS}}$ scheme, as well as the mixing coefficients for the other operators. To this end our computations are performed using dimensional and lattice regularizations. We employ a standard discretization where gluinos are defined on lattice sites and gluons reside on the links of the lattice; the discretization is based on Wilson's formulation of non-supersymmetric gauge theories with clover improvement. The number of colors, $N_c$, the gauge parameter, $\beta$, and the clover coefficient, $c_{\rm SW}$, are left as free parameters.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the mixing of the Gluino-Glue operator in ${\cal N}$=1 Supersymmetric Yang-Mills theory (SYM), both in dimensional regularization and on the lattice. | contribution 0.98 | 0.92 | 0.06 | asserted 0.97 |
| s1 | We calculate its renormalization, which is not only multiplicative, due to the fact that this operator can mix with non-gauge invariant operators of equal or, on the lattice, lower dimension. | result 0.79 | 0.80 | 0.33 | asserted 1.00 |
| s2 | These operators carry the same quantum numbers under Lorentz transformations and global gauge transformations, and they have the same ghost number. | background 0.88 | 0.18 | 0.04 | asserted 1.00 |
| s3 | We compute the one-loop quantum correction for the relevant two-point and three-point Green's functions of the Gluino-Glue operator. | method 0.61 | 0.96 | 0.05 | asserted 1.00 |
| s4 | This allows us to determine renormalization factors of the operator in the $\overline{\textrm{MS}}$ scheme, as well as the mixing coefficients for the other operators. | result 0.93 | 0.94 | 0.33 | asserted 1.00 |
| s5 | To this end our computations are performed using dimensional and lattice regularizations. | method 0.99 | 0.86 | 0.02 | asserted 1.00 |
| s6 | We employ a standard discretization where gluinos are defined on lattice sites and gluons reside on the links of the lattice; the discretization is based on Wilson's formulation of non-supersymmetric gauge theories with clover improvement. | method 1.00 | 0.70 | 0.02 | asserted 1.00 |
| s7 | The number of colors, $N_c$, the gauge parameter, $\beta$, and the clover coefficient, $c_{\rm SW}$, are left as free parameters. | method 0.99 | 0.61 | 0.02 | asserted 0.99 |
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Original abstract
We study the mixing of the Gluino-Glue operator in ${\cal N}$=1 Supersymmetric Yang-Mills theory (SYM), both in dimensional regularization and on the lattice. We calculate its renormalization, which is not only multiplicative, due to the fact that this operator can mix with non-gauge invariant operators of equal or, on the lattice, lower dimension. These operators carry the same quantum numbers under Lorentz transformations and global gauge transformations, and they have the same ghost number. We compute the one-loop quantum correction for the relevant two-point and three-point Green's functions of the Gluino-Glue operator. This allows us to determine renormalization factors of the operator in the $\overline{\textrm{MS}}$ scheme, as well as the mixing coefficients for the other operators. To this end our computations are performed using dimensional and lattice regularizations. We employ a standard discretization where gluinos are defined on lattice sites and gluons reside on the links of the lattice; the discretization is based on Wilson's formulation of non-supersymmetric gauge theories with clover improvement. The number of colors, $N_c$, the gauge parameter, $\beta$, and the clover coefficient, $c_{\rm SW}$, are left as free parameters.
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References
How the literature uses it
9 arXiv papers cite this in 18 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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We compute at one-loop order the renormalization of the Gluino-Glue operator and all operator mixing coefficients.
Perturbative study of the Gluino-Glue operator in SYM · 0.93
Papers citing it · 10 sentences without a confident label
Uses its data or values 1 paper
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The first three renormalization factors are computed in Ref. [ref] ; for a self-contained presentation, they are shown below: [equation] In Ref. [ref] we calculate $Z_c^L,$, using Wilson gluinos without clover term.
Perturbative renormalization of the supercurrent operator in lattice ${\cal N}{=}1$ supersymmetric Yang-Mills theory · Results for Green's functions and for the mixing matrix in the lattice regularization (LR) · 0.83
Compares with it 3 papers
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Our results for $Z_ij^,$, $Z_𝒪^,$ read Z_SS^, = 1 + 𝒪 (g^4), Z_ST^, = 𝒪 (g^4), Z_TS^, = 3 N_c/2 ε + 𝒪 (g^4), Z_TT^, = 1 - 3 N_c/ε + 𝒪 (g^4), Z_𝒪^, = 1 - 3 N_c/ε + 𝒪 (g^4), which agree with our recent one-loop calculations in Refs. [ref] .
Supercurrent renormalization of $\mathcal{N}=1$ supersymmetric Yang-Mills theory on the lattice · Perturbative results in dimensional regularization and conversion factors to · 0.83
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The extraction of the correct renormalization in the $$ scheme, already known in Ref. [ref] for the operator $O_Gg$ is a consistency check of our results.
Gauge-invariant Renormalization of the Gluino-Glue operator · Formulation and $$ calculation · 0.95
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Our results for $Z_ij^,$, $Z_𝒪^,$ read: Z_SS^, = 1 + 𝒪 (g^4), Z_ST^, = 𝒪 (g^4), Z_TS^, = 3 N_c/2 ε + 𝒪 (g^4), Z_TT^, = 1 - 3 N_c/ε + 𝒪 (g^4), Z_𝒪^, = 1 - 3 N_c/ε + 𝒪 (g^4), which agree with our recent one-loop calculations of Refs. [ref] , where gauge-noninvariant Green's functions of all mixing operators with external elementary fields are considered.
Nonperturbative renormalization of the supercurrent in $\mathcal{N} = 1$ Supersymmetric Yang-Mills Theory · One-loop calculation in the MS bar scheme · 0.99
Cites it as background 2 papers
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Furthermore, perturbative investigations using specific regulators, e.g., [ref] , have contributed to precise determinations of counterterms, fine-tuning of parameters, and the renormalization of SUSY operators.
Supersymmetric QCD on the lattice: Fine-tuning and counterterms for the quartic couplings · Introduction · 0.85
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The explicit definitions of $U_plaq.$, $U_rect.$, $F̂_μν^αβ$ in terms of link variables $U_μ(x)$, and the covariant derivatives are standard; they can be found in, e.g. Ref. [ref] .
Nonperturbative renormalization of the supercurrent in $\mathcal{N} = 1$ Supersymmetric Yang-Mills Theory · The action of supersymmetric Yang-Mills theory · 0.92
What it cites · 30 sentences without a confident label
Uses data or values from 1 paper
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The ghost field renormalization constant, $Z_c$, is the same as in Ref. [ref] .
Supersymmetric QCD on the Lattice: An Exploratory Study · Calculation setup · 0.86
Compares with 1 paper
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Since we used the clover action for gluino fields, $Z_λ$ and $Z_u$ are recalculated, leading to[For brevity, decimal numbers in our results are presented only with four digits after the decimal point; they are known to higher accuracy.]: [equation] [equation] which coincide with the expressions in Ref. [ref] for $c_SW=0$ and $N_f=0$.
Supersymmetric QCD on the Lattice: An Exploratory Study · Lattice Regularization · 0.98
Cites as background 4 papers
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All the details and definitions of the continuum and the lattice actions can be found in Ref. [ref] .
Supersymmetric QCD on the Lattice: An Exploratory Study · Lattice Regularization · 0.81
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A further direction in this context regards supersymmetric Ward identities in order to study the lattice artifacts and the recovery of supersymmetry in the continuum limit [ref] .
Continuum extrapolation of Ward identities in $\mathbf{\mathcal{N}=1}$ supersymmetric SU(3) Yang-Mills theory · Summary and Future Plans · 0.89
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Supersymmetry (SUSY) has a long history as a viable extension of the Standard Model [ref] .
Cambridge Lectures on Supersymmetry and Extra Dimensions · Introduction · 1.00
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