Reconnection of Colliding Cosmic Strings

TL;DR

The paper tackles reconnection of cosmic strings by contrasting two effective theories: vortex strings described by a 1+1D Higgs-based sigma model with FI parameter-induced Higgsing, and D-strings described by the D-string action with tachyonic instabilities at intersections. It shows vortex strings reconnect classically for small collision velocity and angle, and derives an analytic velocity upper bound from a geometric analysis on the moduli-space-induced cone, consistent with prior field-theory results. By contrast, D-strings reconnection is shown to be probabilistic, computed via time-dependent tachyon condensation on the D-string worldvolume, and yielding a nonperturbative reconnection probability that mirrors worldsheet results. The study clarifies that the qualitative difference originates from the distinct effective theories on the strings and has potential cosmological implications for distinguishing fundamental D-strings from vortex strings in observational data.

Abstract

For vortex strings in the Abelian Higgs model and D-strings in superstring theory, both of which can be regarded as cosmic strings, we give analytical study of reconnection (recombination, inter-commutation) when they collide, by using effective field theories on the strings. First, for the vortex strings, via a string sigma model, we verify analytically that the reconnection is classically inevitable for small collision velocity and small relative angle. Evolution of the shape of the reconnected strings provides an upper bound on the collision velocity in order for the reconnection to occur. These analytical results are in agreement with previous numerical results. On the other hand, reconnection of the D-strings is not classical but probabilistic. We show that a quantum calculation of the reconnection probability using a D-string action reproduces the nonperturbative nature of the worldsheet results by Jackson, Jones and Polchinski. The difference on the reconnection -- classically inevitable for the vortex strings while quantum mechanical for the D-strings -- is suggested to originate from the difference between the effective field theories on the strings.

Figures (14)

• Figure 1: Reconnection of strings.
• Figure 2: The brane configuration relevant for the Abelian Higgs model. (a) On the D4-brane suspended between parallel NS5-branes, 4 dimensional ${\cal N}=2$ U(1) theory is realized. (b) The FI term is turned on, and the effective theory is the Abelian Higgs model. The dashed line ending on the D4-branes shows a D2-brane (on a "flavor" D6-brane) which is identified with a vortex string. (c) The D2-brane (dashed line) is in a Coulomb phase of its effective field theory. Because it can freely move away from the D4-brane, there is no solitonic interpretation in 3+1 dimensions.
• Figure 3: (a) Initial motion of the two vortex strings (the thick line and the dashed thick line with arrows indicating their orientations). Small arrows show the direction of the motion. (b) Projection of (a) onto the plane spanned by the complex coordinate $z$. The dashed line is a mirror partner of the thick line. (c) Configuration of (a)(b) mapped onto the plane spanned by $\widetilde{z}$.
• Figure 4: The moduli space metric is an induced metric on a 2 dimensional surface embedded in the 3 dimensional $f$-$\widetilde{z}$ space. This surface is a smoothed cone of a deficit angle $\pi$.
• Figure 5: (a) The initial configuration of the Polyakov string (the thick line with an arrow) on the cone corresponding to two straight vortex strings colliding. The small arrows show the direction of the motion of the Polyakov string. (b) The Polyakov string travels without feeling any singularity through the top of the cone, and arrives at the final configuration.