تقرير
Signed distributions of real tensor eigenvectors of Gaussian tensor model via a four-fermi theory
| العنوان: | Signed distributions of real tensor eigenvectors of Gaussian tensor model via a four-fermi theory |
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| المؤلفون: | Sasakura, Naoki |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics High Energy Physics - Theory Mathematical Physics |
| مصطلحات موضوعية: | High Energy Physics - Theory, Mathematical Physics |
| الوصف: | Eigenvalue distributions are important dynamical quantities in matrix models, and it is a challenging problem to derive them in tensor models. In this paper, we consider real symmetric order-three tensors with Gaussian distributions as the simplest case, and derive an explicit formula for signed distributions of real tensor eigenvectors: Each real tensor eigenvector contributes to the distribution by $\pm 1$, depending on the sign of the determinant of an associated Hessian matrix. The formula is expressed by the confluent hypergeometric function of the second kind, which is obtained by computing a partition function of a four-fermi theory. The formula can also serve as lower bounds of real eigenvector distributions (with no signs), and their tightness/looseness are discussed by comparing with Monte Carlo simulations. Large-$N$ limits are taken with the characteristic oscillatory behavior of the formula being preserved. Comment: 11 pages, 2 figures. Paragraphs added in the introduction, and related references added |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.physletb.2022.137618 |
| URL الوصول: | http://arxiv.org/abs/2208.08837 |
| رقم الأكسشن: | edsarx.2208.08837 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.physletb.2022.137618 |
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