Bootstrapping Yang-Mills matrix integrals

Fuente: arXiv
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Main Authors: Li, Wenliang, Su, Xinran
Format: Preprint
Published: 2025
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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
id 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