Virasoro operators in the continuous basis of string field theory

TL;DR

This paper develops analytical tools for the  basis in string field theory, deriving the spectral density and expressing Virasoro generators as delta functions with complex arguments, aiding in the understanding of string symmetries.

Contribution

It provides an explicit analytical form of the spectral density and the matter Virasoro generators in the  basis, advancing computational methods in string field theory.

Findings

Analytical expression for the finite spectral density .

Virasoro generators expressed as delta functions with complex arguments.

Applicable to both matter and ghost sectors.

Abstract

In this work we derive two important tools for working in the \kappa basis of string field theory. First we give an analytical expression for the finite part of the spectral density \rho_{fin}. This expression is relevant when both matter and ghost sectors are considered. Then we calculate the form of the matter part of the Virasoro generators L_n in the \kappa basis, which construct string field theory's derivation Q_{BRST}. We find that the Virasoro generators are given by one dimensional delta functions with complex arguments.