Thermofield Theory of Large $N$ Matrix Models

TL;DR

This work develops a large-$N$ matrix thermofield framework built on a doubled Schwinger-Keldysh contour to access finite-temperature physics and correlation functions. Central to the approach is a collective, loop-space representation with $H_-$ and $H_+$ and a nonlinear collective potential, enabling numerical master-field optimization to obtain thermal backgrounds and loop values. A key contribution is the identification of a thermal Bogoliubov-like symmetry generated by $G_f$ that preserves loop-length and yields exact transformations in the free theory, along with a dynamical symmetry extension to interacting models via constraint equations and a robust numerical scheme. The results include explicit transformations within loop subspaces, verification of KMS conditions at $O(1)$, and practical methods to extract thermal energies, loop values, and spectra, providing a nonperturbative handle on thermodynamics of large-$N$ matrix models with potential holographic relevance.

Abstract

We develop analytical and numerical methods for the matrix thermofield in the large $N$ limit. Through the double collective representation on the Schwinger-Keldysh contour, it provides thermodynamical properties and finite temperature correlation functions, for large $N$ matrix quantum systems.

Figures (12)

• Figure 1: Thermal energy versus the inverse temperature $\beta$.
• Figure 2: Loop values versus the inverse temperature $\beta$.
• Figure 3: Comparison of $E$ vs $y \equiv \phi(M_1 M_2)$, $E$ vs $T$, and $y$ vs $T$ for $g=2$.
• Figure 4: Comparison of $E$ vs $y \equiv \phi(M_1 M_2)$, $E$ vs $T$, and $y$ vs $T$ for $g=10$.
• Figure 5: Comparison of $E$ vs $y \equiv \phi(M_1 M_2)$, $E$ vs $T$, and $y$ vs $T$ for $g=50$.