REVIEW
Collisions of Cosmic F- and D-strings
High Energy Physics - Theory · Submitted 25 May 2004 · 46 references
Pith's verdict: The world-sheet amplitudes in §§3–5 are solid and worth citing; the compactification numbers in §7–8 are where the soft spots live, including a sign slip in eq. (7.20).
T0 · AI review
Why Pith says this
Highlight any text to comment on it.
Referee report
The paper
The paper claims
Cosmic F- and D-strings should usually reconnect less often than gauge-theory cosmic strings, and the amount can be computed from string perturbation theory.
The reading
What carries the argument
The load-bearing device is the use of the optical theorem to convert a reconnection probability into the imaginary part of a forward string amplitude, with the string wrapped on a torus so that the external states are simple winding ground states. That converts three physically distinct collision problems into three standard world-sheet topologies: sphere for F–F, disk for F–$(p,q)$, and annulus for D–D. The Regge limit of these amplitudes is normalized by matching the $1/t$ pole to graviton exchange in effective field theory, and the imaginary part arises from the continuation of $(-s)^{alpha' t/4}$ to Lorentzian momenta. A second piece of machinery, in section 7, is the one-loop world-sheet computation of the transverse spread $langle Y^i Y^i rangle = alpha' omega_i/(2 nu(0))$ with $omega_i = ln[1+nu(0)/(2 pi alpha'^2 H^{1/2} V_{,ii})]$, which turns the geometric compactification volume into an effective wavefunction density $V_{min} rho$ that depends only on the cube of a logarithm of the ratio of the localizing-potential scale to the string scale.
Extended reading notes
Core claim
The paper's claim is that the reconnection probability $P$ for cosmic strings made of F- and D-strings is a calculable, model-dependent number that is generically below one, and in most compactifications small enough to be distinguished from the $P=1$ of gauge-theory solitonic strings. The calculation is done by a unitarity trick: wrap the colliding strings on a large torus, so that reconnection becomes an ordinary closed-string scattering process, and read the total interaction probability off the imaginary part of the forward amplitude. F–F collisions give a sphere amplitude and yield $P = g_s^2 (V_{min}/V_oplus) f(theta,v)$ with $f$ a known kinematic function that vanishes in the supersymmetric limit; F–$(p,q)$ collisions give a disk amplitude with a similar structure but a numerator depending on the electric flux $f$ on the D-string; D–D collisions give an annulus amplitude whose inelastic probability has a Schwinger pair-production form, dominated by the lightest stretched open strings. Because the flat-space answers scale as $V_{min}/V_oplus$, the authors then argue that in a realistic compactification the relevant $V_oplus$ is not the geometric volume but an effective one, set by the logarithmically enhanced quantum spreading of the string in its transverse potential well, so the suppression is only logarithmic and not a huge power. Putting numbers in for the warped-throat and large-dimension models gives $P$ between roughly $10^{-3}$ and $1$ for F-strings and $0.1$ to $1$ for D-strings.
Load-bearing premise
The numerical claim that these strings can be told apart from gauge-theory strings rests on being able to combine the flat-spacetime collision amplitudes with an effective transverse volume computed from logarithmic quantum fluctuations, which is only valid when the potential that localizes the string in the compact directions varies slowly compared with the string scale; if that potential is steep, the flat-space calculation does not apply and the paper leaves the reconnection probability unconstrained.
Editorial extensions
If this is right
- A cosmic string network built from F-strings should be denser than a gauge-theory network by roughly a factor $1/P$, since long strings need reconnection to decay; for $P$ near $10^{-3}$ that is a large, in principle observable, change in the number of long strings.
- The kinkiness and self-intersection rate of the strings should also scale with $P$, so the loop-production rate per long string stays fixed while the spectrum of kink angles carries an imprint of the velocity and angle dependence of $f(theta,v)$.
- Whether two different $(p,q)$ string species intercommute depends sensitively on where their potential minima sit in the compact directions; if the minima are separated by more than a string length the cross-species probability is exponentially suppressed and the two networks evolve independently.
- D–D reconnection is suppressed nonperturbatively, as $e^{-O(1/g_s)}$, once $g_s$ falls below roughly the GUT value, because reconnecting the heavy D-strings requires producing of order $1/g_s$ F-string pairs at the crossing.
- The results supply the $P$ values that network simulations need; the authors list as the natural next steps runs with a single string type at fixed $P$ down to $10^{-3}$, and runs with several $(p,q)$ species starting from a tangled initial state.
Reading between the lines
- The distinguishability claim rests on a chain of two approximations — flat-space collision amplitudes and a Gaussian effective transverse density — so a sharper test would be to repeat the section 7 wavefunction calculation for a modulus potential that varies on the string scale, where the authors themselves say the method breaks down and $P$ is left unconstrained.
- Because the F–$(p,q)$ probability is enhanced relative to F–F by powers of $2^{k/2}/g_s$ when the strings share a minimum but exponentially suppressed when they do not, the transverse localization pattern, not the string coupling, may be the single most consequential unknown for multi-species networks.
- The paper notes but does not resolve the mismatch between the D–D small-velocity result and the F–F result at $g_s=1$, where the two should coincide by duality; a unitarized eikonal treatment of the $1/v$ divergence in the F–F probability is the natural place to look for the missing interpolation.
- If the effective-volume argument is right, the suppression of $P$ saturates at a cube of a logarithm, which means no choice of large extra dimensions can drive the reconnection probability to zero — a prediction that distinguishes this picture from naive geometric intuition about strings missing each other in a big transverse space.
Original abstract
Recent work suggests that fundamental and Dirichlet strings, and their (p,q) bound states, may be observed as cosmic strings. The evolution of cosmic string networks, and therefore their observational signals, depends on what happens when two strings collide. We study this in string perturbation theory for collisions between all possible pairs of strings; different cases involve sphere, disk, and annulus amplitudes. The result also depends on the details of compactification; the dependence on ratios of scales is only logarithmic, but this is still numerically important. We study a range of models and parameters, and find that in most cases these strings can be distinguished from cosmic strings that arise as gauge theory solitons.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
Recent work suggests that fundamental and Dirichlet strings, and their (p,q) bound states, may be observed as cosmic strings. The evolution of cosmic string networks, and therefore their observational signals, depends on what happens when two strings collide. We study this in string perturbation theory for collisions between all possible pairs of strings; different cases involve sphere, disk, and annulus amplitudes. The result also depends on the details of compactification; the dependence on ratios of scales is only logarithmic, but this is still numerically important. We study a range of models and parameters, and find that in most cases these strings can be distinguished from cosmic strings that arise as gauge theory solitons.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recent work suggests that fundamental and Dirichlet strings, and their (p,q) bound states, may be observed as cosmic strings. | background 1.00 | 0.03 | 0.04 | hedged possibility 1.00 |
| s1 | The evolution of cosmic string networks, and therefore their observational signals, depends on what happens when two strings collide. | background 0.96 | 0.06 | 0.04 | asserted 1.00 |
| s2 | We study this in string perturbation theory for collisions between all possible pairs of strings; different cases involve sphere, disk, and annulus amplitudes. | method 0.80 | 0.95 | 0.06 | asserted 0.98 |
| s3 | The result also depends on the details of compactification; the dependence on ratios of scales is only logarithmic, but this is still numerically important. | result 0.90 | 0.66 | 0.06 | asserted 1.00 |
| s4 | We study a range of models and parameters, and find that in most cases these strings can be distinguished from cosmic strings that arise as gauge theory solitons. | result 0.98 | 0.96 | 0.74 | asserted 0.96 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:hep-th/0405229 by the authors.
References
How later papers used it
79 later papers cite it
2 later papers by other authors are listed below: 1 used its method or tool and 1 cited it as support. 1 more paper by the same authors is listed: 1 used its method or tool.
Uses its method or tool 2 papers · 1 by the same authors
-
Following [ref] we parametrise the effects of extra dimensions through a single volume parameter $w$, defined [ref] as the ratio of the minimum volume, $V_min$, that can be occupied by the string in the extra dimensions (this can be roughly thought of as the string thickness raised to the number of compact extra dimensions [ref] ), over the total volume available to the fundamental strings, $V_FF$, which is bounded above by the volume of the compact dimensions.
The stochastic gravitational wave background from cosmic superstrings (2025) · String Dynamics · 0.92
By the same authors
-
Performed the same averaging of poles into a branch cut as this paper did to utilize the optical theorem.
Interactions of Cosmic Superstrings (2007) (same authors) · 0.97 · paraphrased: the licence does not allow quoting
Cites it as support 1 of 2 papers with this label
-
Argued that F-strings should dominate the loop number density because they typically have the smallest reconnection probabilities, citing this paper.
Cosmic Super-Strings and Kaluza-Klein Modes (2012) · 0.98 · paraphrased: the licence does not allow quoting
How the literature uses it
76 arXiv papers cite this in 154 sentences
Papers citing it · 99 sentences without a confident label
Builds on it 1 paper
-
The work in [ref] extended this approach analysing the collisions of fundamental and Dirichlet strings, as well as their (p, q) bound states and also between all possible pairs of strings.
Seeking String Theory in the Cosmos · Intercommuting properties · 0.86
Uses its method or tool 2 papers
-
This formalism also allows us to make contact with the use of the optical theorem [ref] [ref] , written [equation] where $Δ$ is the closed string propagator with Feynman $i ϵ$ prescription, [equation] Let us now trade the (anti)holomorphic operators $L_0, L̃_0$ for the worldsheet hamiltonian $H$ and momentum $P$ operators: [equation] The propagator can then be written as [equation] This is then identical to the expression given above.
Interactions of Cosmic Superstrings · A Better Way to Do This · 0.84
-
Following [ref] we parametrise the effects of extra dimensions through a single volume parameter $w$, defined [ref] as the ratio of the minimum volume, $V_min$, that can be occupied by the string in the extra dimensions (this can be roughly thought of as the string thickness raised to the number of compact extra dimensions [ref] ), over the total volume available to the fundamental strings, $V_FF$, which is bounded above by the volume of the compact dimensions.
The stochastic gravitational wave background from cosmic superstrings · String Dynamics · 0.92
Uses its data or values 6 papers
-
Typical values of the reconnection probabilities obtained in [ref] are in the ranges $10^-3 ≲p ≲1$ for F-strings and $10^-1 ≲p ≲1$ for D-strings.
Cosmic Super-Strings and Kaluza-Klein Modes · Consequences for the Loop Number Density and the Friction-Dominated Epoch · 0.94
-
For ordinary cosmic strings, $p=1$, and it has been estimated as $10^-3 ⩽p ⩽1$ for cosmic F- and D-strings [ref] .
Cosmic Strings as Emitters of Extremely High Energy Neutrinos · Loop distribution · 0.93
-
Even though these are not known, for a large number of models it was found [ref] that the reconnection probability for F-F collisions lies in the range between $10^-3$ and 1.
Cosmic Strings and Cosmic Superstrings · Differences between Cosmic Strings and Cosmic Superstrings · 0.81
Compares with it 2 papers
-
This is consistent with the recent study [ref] for cosmic superstrings [ref] .
Dark baryon from pure Yang-Mills theory and its GW signature from cosmic strings · Gravitational waves from cosmic strings · 0.85
-
This is similar to the case of a D1-brane formed after a brane inflation [ref] , where the coefficient, $c$, depends on the relative velocities and relative angles of the strings [ref] .
Cosmic F- and D-strings from pure Yang-Mills theory · D-strings in SO($N$) · 0.93
Cites it as support 2 papers
-
When different kinds of strings are present and interact, we expect the F-strings to dominate the loop number density, because they typically have the smallest reconnection probabilities [ref] .
Cosmic Super-Strings and Kaluza-Klein Modes · Constraints from Big-Bang Nucleosynthesis, the Diffuse Gamma-Ray Background and GW Experiments · 0.98
-
Actually, the intercommutation probability of our cosmic strings is suppressed by a factor of $1/N^2$ or $e^-cN$, where $c = 𝒪(1)$, in a large-$N$ limit, and can be much smaller than unity [ref] .
Cosmic F- and D-strings from pure Yang-Mills theory · Introduction · 0.96
Cites it as background 31 papers
-
The theory of cosmic superstring reconnection was developed in [ref] [ref] [ref] .
Gravitational Wave Bursts from Cosmic Superstring Reconnections · Basic Process · 0.89
-
Let us thus review [ref] , which considered warping (while neglecting possible effects due to flux).
Gravitational Waves from High Temperature Strings · Review of the JJP box · 0.91
-
For more details on $w$ and its interpretation, see [ref] .
The stochastic gravitational wave background from cosmic superstrings · String Dynamics · 0.93
Discussion
Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.