Collisions of Strings with Y Junctions

Abstract

We study the dynamics of Nambu-Goto strings with junctions at which three strings meet. In particular, we exhibit one simple exact solution and examine the process of intercommuting of two straight strings, in which they exchange partners but become joined by a third string. We show that there are important kinematical constraints on this process. The exchange cannot occur if the strings meet with very large relative velocity. This may have important implications for the evolution of cosmic superstring networks and non-abelian string networks.There has been renewed interest in cosmic strings, both because of tentative observational evidence [1,2] and because they appear to arise naturally in scenarios based on string theory [3,4,5], as well as in field theories [6,7]. Although the recent close inspection by the Hubble Space Telescope of the area of interest in [1, 2] appears to indicate that no string is present [8], the possibility remains that strings may be found through other types of observation in the Universe. Moreover, in the scenarios based on string theory, several different kinds of cosmic strings may appear, in particular F-and D-strings and (p, q) composites, formed of p F-strings and q D-strings [9]. In such cases, junctions may form at which three different strings meet. Such junctions can also appear in networks of 'non-Abelian strings', for which the fundamental group π 1 (M) of the manifold of degenerate vacua, which classifies the strings, is non-Abelian [10,11]. Several papers have considered the evolution of networks of strings with junctions [12,13,14,15], in particular the question of whether such a network would evolve to a scaling regime as expected for an ordinary cosmic-string network [16].In this paper, we study the dynamics of three-string junctions in a local-string network, that is to say one where the individual strings have no long-range interactions and are well described by the Nambu-Goto action. Our approach is similar to the one adopted by 't Hooft in Ref. [17], in which he represented baryons as pieces of open string connected at one common point. However, our method differs from his in significant ways. In particular, our treatment applies to strings with different tensions, and we use a temporal world-sheet coordinate equal to the global time. For ordinary cosmic strings, the existence of exact solutions for oscillating string loops [18,19] was important in analyzing the likely behavior of loops in general, and some exact solutions are also known for open strings with junctions. Here we give one very simple example of an exact solution, but our main focus is on the question of what happens when two strings cross.When two ordinary cosmic strings intersect they normally 'intercommute', or exchange partners [20,21,22,23,24]. But for the strings we are considering this is generally impossible. What we expect instead is that the strings will become joined by a third string. The dynamical problem of finding the intercommuting probability for junction-forming strings has been dis...

Lumps in the throat

“…This coresponds to h 4 → h 4 X ′2 i in Eq(2.5), where ′ indicates differentiation with respect to σ. Following the formalism of [13], the action of the system of three (p, q)-strings to form a Y-shaped junction is…”

“…The equation of motion for the fields X s i is 13) which yields the following boundary condition at σ = 0:…”

“…Furthermore for the simplest scenario with local square tori, there are further approximate simplifications: 13) which are approximate because in the geometric transition set-up the base tori do not seem to have the same complex structures, although on the other hand in the Klebanov-Strassler case the equality is exact. Our scenario lies halfway between these two pictures, and therefore we do not expect exact equality in Eq.…”

“…(4.2)) 13 , and the relevant line element in region A can now be easily determined because we can solve the set of equations (4.35) in terms of a 0 and b 0 to give us:…”

“…In [13] the kinematical constraint on string intercommutation for a network with string junctions was studied. It was shown that two different types of string may not necessarily reconnect into a third string.…”