Classical Limit of Higher-Spin String Amplitudes

TL;DR

This paper compares string theory amplitudes involving massive spinning states with classical black hole and string solutions, revealing differences in classical limits and the necessity of infinite spin for certain reproductions.

Contribution

It provides a comprehensive analysis of the classical limits of string amplitudes, contrasting them with black hole and string solutions, and highlights the role of infinite spin in reproducing classical multipoles.

Findings

String amplitudes match Kerr black hole stress-energy tensor in certain cases.

All-spin results align with classical string coupled to electromagnetism and gravity.

Infinite spin limit is required to reproduce classical spin multipoles in superstring amplitudes.

Abstract

It has been shown that a special set of three-point amplitudes between two massive spinning states and a graviton reproduces the linearised stress-energy tensor for a Kerr black hole in the classical limit. In this work we revisit this result and compare it to the analysis of the amplitudes describing the interaction of leading Regge states of the open and closed superstring. We find an all-spin result for the classical limit of two massive spinning states interacting with a photon or graviton. This result differs from Kerr and instead matches the current four-vector and the stress-energy tensor generated by a classical string coupled to electromagnetism and gravity respectively. For the superstring amplitudes, contrary to the black-hole case, we find that the spin to infinity limit is necessary to reproduce the classical spin multipoles.