Constraints on string networks with junctions

TL;DR

This paper investigates the dynamics and constraints of string networks with junctions, focusing on wave propagation, collision outcomes, and global network properties, revealing conditions for string reconnection and implications for network evolution.

Contribution

It provides new insights into the kinematic constraints and global dynamics of string networks with junctions, especially for diverse string tensions and collision scenarios.

Findings

Strings with equal tensions pass through at high velocities.

Different tension strings can reconnect depending on collision angle and speed.

Junction velocities are generally lower than in networks without junctions.

Abstract

We consider the constraints on string networks with junctions in which the strings may all be different, as may be found for example in a network of $(p,q)$ cosmic superstrings. We concentrate on three aspects of junction dynamics. First we consider the propagation of small amplitude waves across a static three-string junction. Then, generalizing our earlier work, we determine the kinematic constraints on two colliding strings with different tensions. As before, the important conclusion is that strings do not always reconnect with a third string; they can pass straight through one another (or in the case of non-abelian strings become stuck in an X configuration), the constraint depending on the angle at which the strings meet, on their relative velocity, and on the ratios of the string tensions. For example, if the two colliding strings have equal tensions, then for ultra-relativistic initial velocities they pass through one another. However, if their tensions are sufficiently different they can reconnect. Finally, we consider the global properties of junctions and strings in a network. Assuming that, in a network, the incoming waves at a junction are independently randomly distributed, we determine the r.m.s. velocities of strings and calculate the average speed at which a junction moves along each of the three strings from which it is formed. Our findings suggest that junction dynamics may be such as to preferentially remove the heavy strings from the network leaving a network of predominantly light strings. Furthermore the r.m.s. velocity of strings in a network with junctions is smaller than 1/\sqrt{2}, the result for conventional Nambu-Goto strings without junctions in Minkowski spacetime.