Bootstrapping Yang-Mills matrix integrals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909831028277248 |
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| author | Li, Wenliang Su, Xinran |
| author_facet | Li, Wenliang Su, Xinran |
| contents | We revisit the large $N$ limit of bosonic $D$-matrix Yang-Mills integrals using two complementary bootstrap methods. In the positivity bootstrap, we obtain bounds for $\langle \text{tr}\, XX \rangle$ and $\langle \text{tr}\, XXXX \rangle$ at various length cutoff $L_{\max}$. For $D=3$, we do not find an isolated region until $L_{\max}=12$. For larger $D$, the allowed regions become islands at $L_{\max}=8$ and shrink rapidly as $L_{\max}$ increases. The precision of some $L_{\max}=12$ islands is comparable to that of Monte Carlo estimates. For a fixed $L_{\max}$, the allowed region also shrinks with $D$ and converges to the large $D$ expansion results. We further deduce the analytic expressions of various types of trajectories and eigenvalue distributions at large $D$. Based on these explicit formulas, we propose some ansatz for the analytic trajectory bootstrap and obtain accurate results for finite $D$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_06704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bootstrapping Yang-Mills matrix integrals Li, Wenliang Su, Xinran High Energy Physics - Theory High Energy Physics - Lattice We revisit the large $N$ limit of bosonic $D$-matrix Yang-Mills integrals using two complementary bootstrap methods. In the positivity bootstrap, we obtain bounds for $\langle \text{tr}\, XX \rangle$ and $\langle \text{tr}\, XXXX \rangle$ at various length cutoff $L_{\max}$. For $D=3$, we do not find an isolated region until $L_{\max}=12$. For larger $D$, the allowed regions become islands at $L_{\max}=8$ and shrink rapidly as $L_{\max}$ increases. The precision of some $L_{\max}=12$ islands is comparable to that of Monte Carlo estimates. For a fixed $L_{\max}$, the allowed region also shrinks with $D$ and converges to the large $D$ expansion results. We further deduce the analytic expressions of various types of trajectories and eigenvalue distributions at large $D$. Based on these explicit formulas, we propose some ansatz for the analytic trajectory bootstrap and obtain accurate results for finite $D$. |
| title | Bootstrapping Yang-Mills matrix integrals |
| topic | High Energy Physics - Theory High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2510.06704 |