Interaction of Tachyons and Discrete States in c=1 2-D Quantum Gravity

TL;DR

This paper investigates the interactions between tachyons and discrete states in c=1 2-D quantum gravity, deriving three-point couplings and constructing an effective action, highlighting the role of cocycle factors.

Contribution

It provides explicit calculations of three-point couplings involving tachyons and discrete states in 2-D quantum gravity with c=1, including the explicit construction of cocycle factors.

Findings

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

Explicit cocycle factors are constructed and shown to be necessary.

An effective action for these couplings is derived.

Abstract

The two-dimensional (2-D) quantum gravity coupled to the conformal matter with $c=1$ is studied. We obtain all the three point couplings involving tachyons and/or discrete states via operator product expansion. We find that cocycle factors are necessary and construct them explicitly. We obtain an effective action for these three point couplings. This is a brief summary of our study of couplings of tachyons and discrete states, reported at the workshop in Tokyo Metropolitan University, December 4-6, 1991.