Quantum Rings and Recursion Relations in 2D Quantum Gravity

TL;DR

This paper explores how tachyon condensate perturbations deform the ground ring structure in 2D string theory, deriving recursion relations that enable computation of all bulk scattering amplitudes.

Contribution

It demonstrates the deformation of the ground ring by tachyon condensates and derives recursion relations for scattering amplitudes, confirming Witten's conjecture.

Findings

Deformation of the ground ring structure by tachyon condensates

Derivation of recursion relations for scattering amplitudes

All bulk amplitudes can be computed using these recursion relations

Abstract

I study tachyon condensate perturbations to the action of the two dimensional string theory corresponding to the c=1 matrix model. These are shown to deform the action of the ground ring on the tachyon modules, confirming a conjecture of Witten. The ground ring structure is used to derive recursion relations which relate (N+1) and N tachyon bulk scattering amplitudes. These recursion relations allow one to compute all bulk amplitudes.