Folds, Bosonization and non-triviality of the classical limit of 2D string theory

TL;DR

This paper explores the complex classical limit of 2D string theory via matrix models, revealing that fold formations in the fermion surface introduce additional classical variables and lead to nontrivial quantum-to-classical transitions.

Contribution

It introduces the role of quantum dispersions as classical variables in the presence of folds, showing a nontrivial classical limit in 2D string theory.

Findings

Folds in the fermion surface require additional variables for description.

Quantum dispersions become classical quantities after fold formation.

Reflection of pulses results in high-energy incoherent quanta with amplified frequency.

Abstract

In the 1-dimensional matrix model one identifies the tachyon field in the asymptotic region with a nonlocal transform of the density of fermions. But there is a problem in relating the classical tachyon field with the surface profile of the fermi fluid if a fold forms in the fermi surface. Besides the collective field additional variables $w_j(x)$ are required to describe folds. In the quantum theory we show that the $w_j$ are the quantum dispersions of the collective field. These dispersions become $O(1)$ rather than $O(\hbar)$ precisely after fold formation, thus giving additional `classical' quantities and leading to a rather nontrivial classical limit. A coherent pulse reflecting from the potential wall turns into high energy incoherent quanta (if a fold forms), the frequency amplification being of the order of the square root of the number of quanta in the incident wave.