Ward Identities of W_{\infty} Symmetry and Higher Genus Amplitudes in 2D String Theory

TL;DR

This paper investigates the Ward identities of W_infinity symmetry in 2D string theory, deriving recursion relations among higher genus amplitudes, and confirms their consistency with matrix model results.

Contribution

It derives non-linear recursion relations for higher genus amplitudes in 2D string theory using W_infinity Ward identities, extending previous results.

Findings

Recursion relations among amplitudes at different genus

Solutions match matrix model predictions

Differences in external leg factors between models

Abstract

The Ward identities of the $W_{\infty}$ symmetry in two dimensional string theory in the tachyon background are studied in the continuum approach. We consider amplitudes different from 2D string ones by the external leg factor and derive the recursion relations among them. The recursion relations have non-linear terms which give relations among the amplitudes defined on different genus. The solutions agree with the matrix model results even in higher genus. We also discuss differences of roles of the external leg factor between the $c_M = 1$ model and the $c_M <1$ model.