Doubling of Scattering Phase Shifts for Two Dimensional Strings

TL;DR

This paper investigates the origin of leg factors in 2D string theory, revealing that string longitudinal modes double the phase shift during high-energy reflections off the Liouville wall, using semiclassical methods.

Contribution

It introduces a semiclassical approach to compute string amplitudes in 2D, showing how longitudinal modes affect phase shifts and providing a general method for amplitude calculation.

Findings

Longitudinal modes double the phase shift in 2D string reflections.

Leg factors correspond to time delays in reflection off the Liouville wall.

A semiclassical method for arbitrary amplitude calculation is developed.

Abstract

We discuss the origin of the leg factors appearing in 2D string theory. Computing in the world sheet framework we use the semiclassical method to study string amplitudes at high energy. We show that in the case of a simplest 2-point amplitude these factors correspond entirely to the time delay for reflection off the Liouville wall. Our semiclassical calculation reveals that the string longitudinal modes, although nonpropagating in 2D spacetime, have the effect of doubling the phase shift. Particular emphasis is put on comparison with the point particle (center of mass) case. A general method is then given for calculating an arbitrary amplitude semiclassically.