UV asymptotics of $n$-point correlators of twist-$2$ operators in SU($N$) Yang-Mills theory
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arXiv
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2022
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| _version_ | 1866911805966647296 |
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| author | Bochicchio, Marco Papinutto, Mauro Scardino, Francesco |
| author_facet | Bochicchio, Marco Papinutto, Mauro Scardino, Francesco |
| contents | The generating functional $\mathcal{W}[J_{\mathcal O}]$ of Euclidean correlators of twist-$2$ operators in SU($N$) Yang-Mills theory admits the 't Hooft large-$N$ expansion: $\mathcal{W}[J_{\mathcal O}]=\mathcal{W}_{sphere}\,\,\,\,[J_{\mathcal O}]+\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}]+ \cdots$. Nonperturbatively, $\mathcal{W}_{sphere} \,\,\,\,[J_{\mathcal O}]$ is a sum of tree diagrams involving glueball propagators and vertices, while $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}]$ is a sum of glueball one-loop diagrams. Moreover, it has been predicted that $\mathcal{W}_{torus } \,\,\,[J_{\mathcal O}]$ should admit the structure of the logarithm of a functional determinant summing glueball one-loop diagrams. We work out in a closed form the ultraviolet (UV) asymptotics of $\mathcal{W}_{sphere} \,\,\,\,[J_{\mathcal O},λ] \sim \mathcal{W}_{asym \, sphere} \,\,\,\,\,\,\,[J_{\mathcal O},λ]$ and $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O},λ] \sim \mathcal{W}_{asym \, torus} \,\,\,\,\,\,[J_{\mathcal O},λ]$ in the coordinate representation as all the coordinates of the correlators are uniformly rescaled by a factor $λ\rightarrow 0$. Remarkably, we verify the above prediction that $\mathcal{W}_{asym \, torus} \,\,\,\,\,\,[J_{\mathcal O},λ]$ -- being asymptotic in the UV to $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}, λ]$ -- admits the structure of the logarithm of a functional determinant as well. Hence, the computation above sets strong UV asymptotic constraints on the nonperturbative solution of large-$N$ YM theory and it may be a pivotal guide for the search of such a solution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_14382 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | UV asymptotics of $n$-point correlators of twist-$2$ operators in SU($N$) Yang-Mills theory Bochicchio, Marco Papinutto, Mauro Scardino, Francesco High Energy Physics - Theory High Energy Physics - Phenomenology The generating functional $\mathcal{W}[J_{\mathcal O}]$ of Euclidean correlators of twist-$2$ operators in SU($N$) Yang-Mills theory admits the 't Hooft large-$N$ expansion: $\mathcal{W}[J_{\mathcal O}]=\mathcal{W}_{sphere}\,\,\,\,[J_{\mathcal O}]+\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}]+ \cdots$. Nonperturbatively, $\mathcal{W}_{sphere} \,\,\,\,[J_{\mathcal O}]$ is a sum of tree diagrams involving glueball propagators and vertices, while $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}]$ is a sum of glueball one-loop diagrams. Moreover, it has been predicted that $\mathcal{W}_{torus } \,\,\,[J_{\mathcal O}]$ should admit the structure of the logarithm of a functional determinant summing glueball one-loop diagrams. We work out in a closed form the ultraviolet (UV) asymptotics of $\mathcal{W}_{sphere} \,\,\,\,[J_{\mathcal O},λ] \sim \mathcal{W}_{asym \, sphere} \,\,\,\,\,\,\,[J_{\mathcal O},λ]$ and $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O},λ] \sim \mathcal{W}_{asym \, torus} \,\,\,\,\,\,[J_{\mathcal O},λ]$ in the coordinate representation as all the coordinates of the correlators are uniformly rescaled by a factor $λ\rightarrow 0$. Remarkably, we verify the above prediction that $\mathcal{W}_{asym \, torus} \,\,\,\,\,\,[J_{\mathcal O},λ]$ -- being asymptotic in the UV to $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}, λ]$ -- admits the structure of the logarithm of a functional determinant as well. Hence, the computation above sets strong UV asymptotic constraints on the nonperturbative solution of large-$N$ YM theory and it may be a pivotal guide for the search of such a solution. |
| title | UV asymptotics of $n$-point correlators of twist-$2$ operators in SU($N$) Yang-Mills theory |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2208.14382 |