Duality and Decay of Macroscopic F-Strings

TL;DR

This paper investigates the decay properties of macroscopic fundamental string loops, demonstrating duality relations, computing decay rates for specific trajectories, and connecting these results with low-energy effective theories to explore string evolution near cusps.

Contribution

It introduces an efficient computational approach for string decay rates using coherent vertex operators and uncovers duality and radiation relations for macroscopic string loops.

Findings

Decay rates of dual string states are equal at leading order.

Power and decay rates for massless radiation match low-energy effective theory predictions.

Discovered a relation between gravitational and axion+dilaton radiation in string decay.

Abstract

We study the decay of fundamental string loops of arbitrary size L/min(n,m)>>\sqrt{\alpha'}, labelled by (n,m;\lambda_n,\bar{\lambda}_m), where n,m correspond to left- and right-mover harmonics and \lambda_n,\bar{\lambda}_m to polarisation tensors, and find that a description in terms of the recent coherent vertex operator construction of Hindmarsh and Skliros is computationally very efficient. We primarily show that the decay rates and mass shifts of vertex operators (n,m;\lambda_n,\bar{\lambda}_m) and their "duals" (n,m;\lambda_n,\bar{\lambda}_m^*) are equal to leading order in the string coupling, implying for instance that decay rates of epicycloids equal those of hypocycloids. We then compute the power and decay rates associated to massless IR radiation for the trajectory (1,1;\lambda_1,\bar{\lambda}_1), and find that it is precisely reproduced by the low energy effective theory of Dabholkar and Harvey. Guided by this correspondence, we conjecture the result for arbitrary trajectories (n,m;\lambda_n,\bar{\lambda}_m) and discover a curious relation between gravitational and axion plus dilaton radiation. It is now possible to start exploring string evolution in regimes where a low energy effective description is less useful, such as in the vicinity of cusps.