Calabi-Yau CFTs and Random Matrices

TL;DR

This paper investigates the spectral properties of Calabi-Yau conformal field theories using numerical Ricci-flat metric methods, revealing their spectra exhibit random matrix statistics similar to GOE, especially in K3 and quintic examples.

Contribution

It demonstrates that the averaged spectrum of certain Calabi-Yau CFTs aligns with random matrix theory, providing new insights into their universal spectral behavior.

Findings

Spectra follow Gaussian orthogonal ensemble statistics

Spectral properties are consistent across K3 and quintic models

Numerical methods effectively analyze Calabi-Yau CFT spectra

Abstract

Using numerical methods for finding Ricci-flat metrics, we explore the spectrum of local operators in two-dimensional conformal field theories defined by sigma models on Calabi-Yau targets at large volume. Focusing on the examples of K3 and the quintic, we show that the spectrum, averaged over a region in complex structure moduli space, possesses the same statistical properties as the Gaussian orthogonal ensemble of random matrix theory.