Ward Identities in Two-Dimensional String Theory

TL;DR

This paper investigates the Ward identities associated with the $w_inf$ symmetry in two-dimensional string theory, revealing how vertex operator collisions affect charge conservation and calculating bulk tachyon amplitudes.

Contribution

It determines the structure of contact terms from vertex operator collisions and computes bulk tachyon amplitudes using Ward identities for a Virasoro subalgebra.

Findings

Vertex operator collisions can cause local charge non-conservation.

Contact terms' structure is fully characterized.

All non-vanishing bulk tachyon amplitudes are calculated.

Abstract

I study the Ward identities of the $w_\infty$ symmetry of the two-dimensional string theory. It is found that, not just an isolated vertex operator, but also a number of vertex operators colliding at a point can produce local charge non-conservation. The structure of all such contact terms is determined. As an application, I calculate all the non-vanishing bulk tachyon amplitudes directly through the Ward identities for a Virasoro subalgebra of the $w_\infty$.