Coupling of Tachyons and Discrete States in $c = 1$ 2-D Gravity

TL;DR

This paper computes all three-point couplings involving tachyons and discrete states in $c=1$ 2-D quantum gravity using operator product expansion, highlighting the necessity of cocycle factors for analytic consistency.

Contribution

It provides explicit calculations of three-point couplings and constructs cocycle factors, advancing understanding of operator algebra in $c=1$ 2-D gravity.

Findings

All three-point couplings involving tachyons and discrete states are obtained.

Cocycle factors are essential for maintaining the analytic structure of the OPE.

An effective action summarizing these couplings is derived.

Abstract

All the three point couplings involving tachyons and/or discrete states are obtained in $c=1$ two-dimensional (2-D) quantum gravity by means of the operator product expansion (OPE). Cocycle factors are found to be necessary in order to maintain the analytic structure of the OPE, and are constructed explicitly both for discrete states and for tachyons. The effective action involving tachyons and discrete states is worked out to summarize all of these three point couplings.