An asymptotic bootstrap method and its applications to Hermitian matrix models

2026/06/29 by David Berenstein, Paula Garcia Martinez
#hep-th

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Abstract

We propose an asymptotic bootstrap method to evaluate moment integrals that arise in problems related to hermitian matrix models. These are normalized integrals of the form a_n=∫^∞_-∞ xⁿ exp(-V(x)) dx where V(x) is a polynomial of x. The method is applicable even when the coupling constants in V(x)= x^2ℓ/(2ℓ) + g_2ℓ-2 x^2ℓ-2/(2ℓ-2) + … are complex. We prove that the method converges asymptotically exponentially fast on a cone region determined by the first subleading coupling g_2ℓ-2, which must have a positive real part and an absolute value of the argument less than π/ℓ. We use our method to study the phase structure of Hermitian matrix models by constructing the orthogonal polynomials associated to these measures.

Citations

• From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
• Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings

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