W_infty Structures of 2D String Theory

TL;DR

This paper investigates the $W_{ abla}$ symmetry in 2D string theory, showing that continuum and matrix model results differ only by external leg factors across different genera, enhancing understanding of 2D string amplitudes.

Contribution

It provides a continuum approach analysis of Ward identities in 2D string theory and compares results with matrix models, confirming their close relationship.

Findings

2D string amplitudes differ from matrix model results only by external leg factors

Verification of Ward identities in the continuum approach

Consistency of higher genus amplitudes between approaches

Abstract

The Ward identities of the $W_{\infty}$ symmetry in 2D string theory in the tachyon background are studied in the continuum approach. Comparing the solutions with the matrix model results, it is verified that 2D string amplitudes are different from the matrix model amplitudes only by the external leg factors even in higher genus. This talk is based on the recent work [1] and also [2] for the $c_M <1$ model. (Talk given at the workshop on ``Frontiers in Quantum Field Theory'', Osaka, Japan, December 1995.)