Photon emission from an excited string

TL;DR

This paper calculates the decay amplitudes of highly excited strings into other states with photon or tachyon emission, revealing complex state-dependent behaviors and connecting to black hole microstates via the Horowitz-Polchinski correspondence.

Contribution

It introduces a method to compute decay amplitudes for arbitrary excited string states using tachyon and photon amplitudes, advancing understanding of string decay processes.

Findings

Amplitude depends on outgoing angle and specific states.

Average squared amplitude computed over polarizations.

Results relate string microstates to black hole microstates.

Abstract

We compute the amplitude for an excited string in any precisely specified state to decay into another excited string in any precisely specified state, via emission of a tachyon or photon. For generic and highly excited string states, the amplitude is a complicated function of the outgoing kinematic angle, sensitive to the precise state. We compute the square of this amplitude, averaged over polarizations of the ingoing string and summed over polarizations of the outgoing string. The seeming intractability of these calculations is made possible by extracting amplitudes involving excited strings from amplitudes involving tachyons and a large number of photons; the number of photons grows with the complexity of the excited string state. Our work is in the spirit of the broad range of recent studies of statistical mechanics and chaos for quantum many-body systems. The number of different excited string states at a given mass is exponentially large, and our calculation gives the emission amplitude of a single photon from each of the microstates -- which, through the Horowitz-Polchinski correspondence principle, are in correspondence with black hole microstates.