String interactions in gravitational wave backgrounds

TL;DR

This paper exactly solves a class of string theories in specific gravitational backgrounds, computes scattering amplitudes, and analyzes their properties and limits, revealing insights into string interactions in curved spacetime.

Contribution

It provides an exact solution for the non-compact CFT of NS-supported pp-wave backgrounds and calculates the associated string scattering amplitudes.

Findings

S-matrix elements are well-defined and dual but non-analytic in $p^+$.

Poles in amplitudes correspond to physical states with $p^+ eq 0$.

Logarithmic branch cuts arise from on-shell spectral-flow states.

Abstract

The non-compact CFT of a class of NS-supported pp-wave backgrounds is solved exactly. The associated tree-level covariant string scattering amplitudes are calculated. The S-matrix elements are well-defined, dual but not analytic as a function of $p^+$. They have poles corresponding to physical intermediate states with $p^+\not =0$ and logarithmic branch cuts due to on-shell exchange of spectral-flow images of $p^+=0$ states. When $\mu\to 0$ a smooth flat space limit is obtained. The $\mu\to\infty$ limit, unlike the case of RR-supported pp-waves, gives again a flat space theory.