Nonperturbative determination of the ${\cal N} = 1$ supersymmetric Yang-Mills gluino condensate at large $N$
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| Format: | Preprint |
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2024
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| _version_ | 1866914964486225920 |
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| author | Bonanno, Claudio Butti, Pietro Pérez, Margarita García González-Arroyo, Antonio Ishikawa, Ken-Ichi Okawa, Masanori |
| author_facet | Bonanno, Claudio Butti, Pietro Pérez, Margarita García González-Arroyo, Antonio Ishikawa, Ken-Ichi Okawa, Masanori |
| contents | We present the first nonperturbative large-$N$ calculation of the $\mathcal{N}=1$ supersymmetric (SUSY) $\mathrm{SU}(N)$ Yang$-$Mills gluino condensate obtained by means of numerical simulations of the lattice-discretized theory, exploiting large-$N$ twisted volume reduction. We present two different determinations based, respectively, on the Banks$-$Casher formula and on the Gell-Mann$-$Oakes$-$Renner relation, both giving perfectly consistent results. By expressing the lattice results in the Novikov$-$Shifman$-$Vainshtein$-$Zakharov (NSVZ) scheme, we are able for the first time to compare numerical and analytic computations. Our most accurate determination of the Renormalization Group Invariant (RGI) gluino condensate gives $Σ_{\rm RGI} /Λ_{\rm NSVZ}^3 = [1.18\, (08)_{\rm stat}\, (12)_{\rm syst}]^3 = 1.64(33)_{\rm stat} \, (50)_{\rm syst} = 1.64(60)$, in agreement with the $N$-dependence and the value predicted by the weak coupling instanton-based approach $Σ_{\rm RGI} /Λ_{\rm NSVZ}^3 = 1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_08995 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonperturbative determination of the ${\cal N} = 1$ supersymmetric Yang-Mills gluino condensate at large $N$ Bonanno, Claudio Butti, Pietro Pérez, Margarita García González-Arroyo, Antonio Ishikawa, Ken-Ichi Okawa, Masanori High Energy Physics - Theory High Energy Physics - Lattice We present the first nonperturbative large-$N$ calculation of the $\mathcal{N}=1$ supersymmetric (SUSY) $\mathrm{SU}(N)$ Yang$-$Mills gluino condensate obtained by means of numerical simulations of the lattice-discretized theory, exploiting large-$N$ twisted volume reduction. We present two different determinations based, respectively, on the Banks$-$Casher formula and on the Gell-Mann$-$Oakes$-$Renner relation, both giving perfectly consistent results. By expressing the lattice results in the Novikov$-$Shifman$-$Vainshtein$-$Zakharov (NSVZ) scheme, we are able for the first time to compare numerical and analytic computations. Our most accurate determination of the Renormalization Group Invariant (RGI) gluino condensate gives $Σ_{\rm RGI} /Λ_{\rm NSVZ}^3 = [1.18\, (08)_{\rm stat}\, (12)_{\rm syst}]^3 = 1.64(33)_{\rm stat} \, (50)_{\rm syst} = 1.64(60)$, in agreement with the $N$-dependence and the value predicted by the weak coupling instanton-based approach $Σ_{\rm RGI} /Λ_{\rm NSVZ}^3 = 1$. |
| title | Nonperturbative determination of the ${\cal N} = 1$ supersymmetric Yang-Mills gluino condensate at large $N$ |
| topic | High Energy Physics - Theory High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2406.08995 |