Handbook on string decay

TL;DR

This paper introduces semi-classical rules to estimate decay lifetimes of highly-excited string states, applies them to specific rotating and pulsating string solutions, and verifies their accuracy through explicit quantum decay rate calculations.

Contribution

It presents a new semi-classical approach for estimating string decay rates and applies it to complex rotating and pulsating string configurations, including the squashing ellipse.

Findings

Validated semi-classical decay estimates against quantum calculations.

Derived decay rates for the squashing ellipse string solution.

Extended analysis to a family of elliptical string solutions.

Abstract

We explain simple semi-classical rules to estimate the lifetime of any given highly-excited quantum state of the string spectrum in flat spacetime. We discuss both the decays by splitting into two massive states and by massless emission. As an application, we study a solution describing a rotating and pulsating ellipse which becomes folded at an instant of time -- the ``squashing ellipse''. This string interpolates between the folded string with maximum angular momentum and the pulsating circular string. We explicitly compute the quantum decay rate for the corresponding quantum state, and verify the basic rules that we propose. Finally, we give a more general (4-parameter) family of closed string solutions representing rotating and pulsating elliptical strings.