Analytic trajectory bootstrap for matrix models

Abstract

We revisit the large $N$ two-matrix model with $\text{tr}[A,B{]}^2$ interaction and quartic potentials by the analytic trajectory bootstrap, where $A$ and $B$ represent the two matrices. In the large $N$ limit, we can focus on the single trace moments associated with the words composed of the letters $A$ and $B$. Analytic continuations in the lengths of the words and subwords lead to analytic trajectories of single trace moments and intriguing intersections of different trajectories. Inspired by the one-cut solutions of one-matrix models, we propose some simple ansatzes for the singularity structure of the two-matrix generating functions and the corresponding single trace moments. Together with the self-consistent constraints from the loop equations, we determine the free parameters in the ansatzes and obtain highly accurate solutions for the two-matrix model at a low computational cost. For a given length cutoff $L_{\text{max}}$, our results are within and more accurate than the positivity bounds from the relaxation method, such as about 6-digit accuracy for $L_{\text{max}}=18$. The convergence pattern suggests that we achieve about $8$-digit accuracy for $L_{\text{max}}=22$. As the singularity structure is closely related to the eigenvalue distributions, we further present the results for various types of eigenvalue densities. In the end, we study the symmetry breaking solutions using more complicated ansatzes.

v2, 32 pages, 9 figures, typos corrected, discussion improved, footnotes added

References in corpus (37)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• A Large-N Reduced Model as Superstring
• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• The Analytic Bootstrap and AdS Superhorizon Locality
• Analyticity in Spin in Conformal Theories
• Convexity and Liberation at Large Spin
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Comments on operators with large spin
• Large Spin Perturbation Theory
• D-particles, Matrix Integrals and KP hierachy
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• Bootstrapping Matrix Quantum Mechanics
• Loop Equations and bootstrap methods in the lattice
• Bootstraps to Strings: Solving Random Matrix Models with Positivity
• Bootstrap for Lattice Yang-Mills theory
• Analytic and Numerical Bootstrap for One-Matrix Model and "Unsolvable" Two-Matrix Model
• New Developments in the Numerical Conformal Bootstrap
• Bootstrapping More QM Systems
• Bootstrap bounds on D0-brane quantum mechanics
• Null bootstrap for non-Hermitian Hamiltonians
• A Semidefinite Programming algorithm for the Quantum Mechanical Bootstrap
• Underdetermined Dyson-Schwinger equations
• Bootstrapping Calabi-Yau Quantum Mechanics
• Application of Bootstrap to $\theta$-term
• Bootstrapping PT symmetric Hamiltonians
• Bootstrap Method in Harmonic Oscillator
• Lower Bounding Ground-State Energies of Local Hamiltonians Through the Renormalization Group
• Bootstrapping microcanonical ensemble in classical system
• Bootstrapping the Kronig-Penney Model
• Taming Dyson-Schwinger equations with null states
• Ising model close to $d=2$
• Dyson-Schwinger equations in zero dimensions and polynomial approximations
• Solving anharmonic oscillator with null states: Hamiltonian bootstrap and Dyson-Schwinger equations
• Principle of minimal singularity for Green's functions
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Semidefinite Programs at Finite Fermion Density

Cited by in corpus (4)

• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Thermofield Theory of Large $N$ Matrix Models
• Bootstrapping periodic quantum systems