String interactions in gravitational wave backgrounds

TL;DR

The paper analyzes string theory in the Penrose limit of NS5-brane backgrounds, yielding a solvable Nappi–Witten (NW) pp-wave described by an $H_4$ current algebra. By solving the Knizhnik–Zamolodchikov equations and employing a quasi-free-field realization, it derives all three- and four-point correlators, including spectral-flowed sectors, and constructs covariant tree-level S-matrix elements that are dual and non-analytic in $p^+$. The amplitudes exhibit poles from physical intermediate states with $p^+\neq 0$ and logarithmic branch cuts from spectral-flow images of $p^+=0$ states, reflecting a continuum of intermediate operators. Two flat-space limits exist: $\mu\to 0$ and $\mu\to\infty$, both yielding a flat theory but with distinct surviving sectors, highlighting the rich stringy structure of NW backgrounds and offering a concrete holographic framework via auxiliary charge coordinates $x,\bar{x}$ for boundary data. The results provide exact, tractable insights into string interactions in time-dependent, non-compact backgrounds and lay groundwork for exploring holography and generalizations to RR pp-waves.

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 $μ\to 0$ a smooth flat space limit is obtained. The $μ\to\infty$ limit, unlike the case of RR-supported pp-waves, gives again a flat space theory.