On the structure of the large-$N$ expansion in SU($N$) Yang-Mills theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911158023225344 |
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| author | Bochicchio, Marco Papinutto, Mauro Scardino, Francesco |
| author_facet | Bochicchio, Marco Papinutto, Mauro Scardino, Francesco |
| contents | Recently, we have computed the short-distance asymptotics of the generating functional of Euclidean correlators of single-trace twist-$2$ operators in the large-$N$ expansion of SU($N$) Yang-Mills (YM) theory to the leading-nonplanar order. Remarkably, it has the structure of the logarithm of a functional determinant, but with the sign opposite to the one that would follow from the spin-statistics theorem for the glueballs. In order to solve this sign puzzle, we have reconsidered the proof in the literature that in the 't Hooft topological expansion of large-$N$ YM theory the leading-nonplanar contribution to the generating functional consists of the sum over punctures of $n$-punctured tori. We have discovered that for twist-$2$ operators it contains -- in addition to the $n$-punctured tori -- the normalization of tori with $1 \leq p \leq n$ pinches and $n-p$ punctures. Once the existence of the new sector is taken into account, the violation of the spin-statistics theorem disappears. Moreover, the new sector contributes trivially to the nonperturbative $S$ matrix because -- for example -- the $n$-pinched torus represents nonperturbatively a loop of $n$ glueball propagators with no external leg. This opens the way for an exact solution limited to the new sector that may be solvable thanks to the vanishing $S$ matrix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the structure of the large-$N$ expansion in SU($N$) Yang-Mills theory Bochicchio, Marco Papinutto, Mauro Scardino, Francesco High Energy Physics - Theory High Energy Physics - Phenomenology Recently, we have computed the short-distance asymptotics of the generating functional of Euclidean correlators of single-trace twist-$2$ operators in the large-$N$ expansion of SU($N$) Yang-Mills (YM) theory to the leading-nonplanar order. Remarkably, it has the structure of the logarithm of a functional determinant, but with the sign opposite to the one that would follow from the spin-statistics theorem for the glueballs. In order to solve this sign puzzle, we have reconsidered the proof in the literature that in the 't Hooft topological expansion of large-$N$ YM theory the leading-nonplanar contribution to the generating functional consists of the sum over punctures of $n$-punctured tori. We have discovered that for twist-$2$ operators it contains -- in addition to the $n$-punctured tori -- the normalization of tori with $1 \leq p \leq n$ pinches and $n-p$ punctures. Once the existence of the new sector is taken into account, the violation of the spin-statistics theorem disappears. Moreover, the new sector contributes trivially to the nonperturbative $S$ matrix because -- for example -- the $n$-pinched torus represents nonperturbatively a loop of $n$ glueball propagators with no external leg. This opens the way for an exact solution limited to the new sector that may be solvable thanks to the vanishing $S$ matrix. |
| title | On the structure of the large-$N$ expansion in SU($N$) Yang-Mills theory |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2401.09312 |