Generating functional of correlators of twist-$2$ operators in $\mathcal{N} = 1$ SUSY Yang-Mills theory, I
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912204590153728 |
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| author | Bochicchio, Marco Papinutto, Mauro Scardino, Francesco |
| author_facet | Bochicchio, Marco Papinutto, Mauro Scardino, Francesco |
| contents | The present paper is the first installment where, extending our previous work in pure Yang-Mills (YM) theory, we compute the generating functional of correlators of collinear twist-$2$ operators that enter the components of balanced superfields -- i.e., superfields with an equal number of dotted and undotted indices in their spinor representation -- in $\mathcal{N} = 1$ SUSY SU($N$) YM theory in Minkowskian and Euclidean space-time, in the conformal limit and renormalization-group (RG) improved form, and to the leading and next-to-leading order in the large-$N$ expansion. Moreover, we compare our asymptotic RG-improved generating functional to the next-to-leading large-$N$ order with the corresponding nonperturbative object arising from the glueball/gluinoball one-loop effective action, which it should be asymptotic to at short distances because of the asymptotic freedom. Remarkably, we find that both have the structure of the logarithm of a functional superdeterminant. Hence, our large-$N$ computation sets strong ultraviolet asymptotic constraints on the nonperturbative solution of large-$N$ $\mathcal{N} = 1$ SUSY YM theory that may be a pivotal guide for the search of such a solution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_09617 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generating functional of correlators of twist-$2$ operators in $\mathcal{N} = 1$ SUSY Yang-Mills theory, I Bochicchio, Marco Papinutto, Mauro Scardino, Francesco High Energy Physics - Theory High Energy Physics - Phenomenology The present paper is the first installment where, extending our previous work in pure Yang-Mills (YM) theory, we compute the generating functional of correlators of collinear twist-$2$ operators that enter the components of balanced superfields -- i.e., superfields with an equal number of dotted and undotted indices in their spinor representation -- in $\mathcal{N} = 1$ SUSY SU($N$) YM theory in Minkowskian and Euclidean space-time, in the conformal limit and renormalization-group (RG) improved form, and to the leading and next-to-leading order in the large-$N$ expansion. Moreover, we compare our asymptotic RG-improved generating functional to the next-to-leading large-$N$ order with the corresponding nonperturbative object arising from the glueball/gluinoball one-loop effective action, which it should be asymptotic to at short distances because of the asymptotic freedom. Remarkably, we find that both have the structure of the logarithm of a functional superdeterminant. Hence, our large-$N$ computation sets strong ultraviolet asymptotic constraints on the nonperturbative solution of large-$N$ $\mathcal{N} = 1$ SUSY YM theory that may be a pivotal guide for the search of such a solution. |
| title | Generating functional of correlators of twist-$2$ operators in $\mathcal{N} = 1$ SUSY Yang-Mills theory, I |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2403.09617 |