On spectral density of Neumann matrices

TL;DR

This paper derives an exact analytic expression for the finite part of the spectral density of Neumann matrices, enabling precise calculations of determinants in string field theory.

Contribution

It provides a new exact formula for the finite spectral density of Neumann matrices, improving the understanding of their spectral properties in string theory.

Findings

Derived an explicit formula for the finite spectral density

Validated the formula through consistency checks

Facilitates accurate determinant calculations in string field theory

Abstract

In hep-th/0111281 the complete set of eigenvectors and eigenvalues of Neumann matrices was found. It was shown also that the spectral density contains a divergent constant piece that being regulated by truncation at level L equals (log L)/(2\pi). In this paper we find an exact analytic expression for the finite part of the spectral density. This function allows one to calculate finite parts of various determinants arising in string field theory computations. We put our result to some consistency checks.