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Cosmic F- and D-strings

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Edmund J. Copeland, Robert C. Myers, Joseph Polchinski

High Energy Physics - Theory · Submitted 5 Dec 2003 · 56 references

Pith's verdict: A careful, mostly qualitative paper whose real contribution is the stability classification, not the numbers; the decay-rate exponents are scaling estimates and the authors know it.

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arXiv IDhep-th/0312067 (version 5)
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CitationEdmund J. Copeland, Joseph Polchinski, Robert C. Myers. "Cosmic F- and D-strings." arXiv:hep-th/0312067 (2003). https://pith.science/paper/FNFFQO5F
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The paper

The paper claims

The paper asks whether the strings of string theory itself — fundamental F-strings, Dirichlet D-strings, and bound $(p,q)$ states — can survive as macroscopic cosmic strings, and argues that they can, provided no brane filling ordinary four

The reading

In 1985 it looked as though string theory's own strings could never be cosmic strings: they were either too heavy, or they broke, or they were dragged into collapse by domain walls. This paper reopens that question in the modern setting of warped compactifications and brane inflation, and asks precisely which instabilities actually operate and when they can be suppressed. The authors identify three ways a long string dies — breaking on a brane that fills ordinary space, tachyonic decay of an unstable brane configuration, and confinement by the domain walls that instantons attach to an axion — and give the condition under which each is evaded. Applied to a leading brane-inflation model, they find that a whole spectrum of $(p,q)$ strings, bound states of $p$ fundamental and $q$ Dirichlet strings, can be metastable, with tensions in the range $10^{-10}$ to $10^{-9}$ in Planck units. The payoff is that cosmic strings become a possible, if model-dependent, window onto string-scale physics, with gravitational-wave observatories named as the instrument that could reach the relevant tensions.

What carries the argument

Three instability channels and one screening mechanism carry the argument. Breaking is governed by whether the string can end on a spacetime-filling brane, which is really a statement about a brane gauge field absorbing the string's charge: the string dissolves into a tube of flux whose energy can spread and vanish on a D3-brane but not on a D5-brane, where the flux is a fixed instanton-like lump. Tachyon decay of an unstable brane pair is suppressed by the separation between the pair. The axion channel uses the fact that a BPS string is a magnetic source for a four-dimensional axion, so an instanton-generated potential forces a domain wall onto the string; the escape is the nonlinear Higgsing of that axion by the brane's $U(1)$, after which the axion is absent from the massless spectrum. The $(p,q)$ tension $2/pi alpha' sqrt((p-Cq)^2 + e^{-2Phi} q^2)$ sets the whole spectrum, and the warped throat supplies the enormous exponential suppression $e^{-B}$ with $B ~ e^{-2A_0} ~ 10^8$ that keeps a D-string from finding its orientifold image.

Extended reading notes

Core claim

The central claim is that metastable macroscopic F-, D- and $(p,q)$ strings exist in many type II compactifications, and that the deciding factor is what branes sit in, or pass through, the region where the strings are produced. Breakage requires a brane that fills the four noncompact dimensions and on which the string can end; a string can end on a D3-brane but not, in any energy-lowering way, on a D5- or D7-brane, and even where breaking is possible it can be suppressed by transverse separation or by a warped geometry. A related instability, the tachyon of a brane–antibrane pair, is suppressed the same way. The axion domain-wall problem is dissolved rather than suppressed: if the axion couples to a brane gauge field, the gauge symmetry eats it, there is no periodic potential to make a wall, and the apparent paradox of a string that both breaks and bounds a wall is resolved because the wall never forms. Applied to the Kachru–Kallosh–Linde–Maldacena–McAllister–Trivedi model, the authors find three outcomes depending on how the Standard Model and stabilizing branes are placed: no strings at all, D-strings only, or a $(p,q)$ spectrum with relatively prime $p,q$ and $|p|$ bounded by half the three-form flux quantum $M$ on the throat's three-sphere, because a wrapped D3-brane ('baryon') lets a $(p,q)$ string decay to a $(p-M,q)$ string.

Load-bearing premise

The D-string's survival rests on an order-of-magnitude estimate, not a computed instanton action: the exponential suppression $B ~ e^{-2A_0} ~ 10^8$ for a worldsheet hole through which the string annihilates with its orientifold image assumes the string sits at the throat tip and that the boundary cost is set by the throat-to-image distance, and a smaller true action would let it decay on a stringy time scale.

Editorial extensions

If this is right

  • Cosmic string searches become a probe of string compactification: which branes are present and where they sit determines whether a string network exists at all, so a detection or a null result constrains model building.
  • In the brane-inflation model the predicted tensions sit at $sqrt(G mu_F G mu_D) ~ 2 times 10^{-10}$ with $mu_D/mu_F = 1/g_s$, i.e. both strings near $10^{-10}$ to $10^{-9}$, below the current CMB bound of about $0.7 times 10^{-6}$ but inside the reach of planned gravitational-wave measurements.
  • Because strings of different type cannot simply reconnect, a $(p,q)$ network has trilinear vertices where a $(p,q)$ and a $(p',q')$ string meet to form a $(p+p',q+q')$ or $(p-p',q-q')$ string; the authors conjecture such networks still scale with the horizon rather than freezing into a $w=-1/3$ state, and note that freezing would exclude the models considered.
  • Intercommutation is not guaranteed: for fundamental strings the reconnection probability is of order $0.5 g_s^2 V_{min}/V$, so a measured probability below unity would be a signature of weakly coupled fundamental strings rather than gauge-theory flux tubes.
  • A measured spectrum of string tensions with more than one species would be evidence for an $SL(2,Z)$ multiplet, though the authors caution that the same spectrum can arise in the dual gauge description of the throat.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's stability logic is essentially a checklist that could be run in reverse: given any proposed string-producing model, listing the four-dimensional-filling branes and asking whether each string can end on one is a cheap filter that does not require solving the full compactification.
  • The Higgsing resolution of the axion puzzle suggests that the presence of a massless axion is itself the diagnostic — a compactification whose moduli include an un-Higgsed two-form has confined strings, one whose two-form is eaten does not, which is a sharper statement than the older lore that all BPS strings are wall-confined.
  • If the $(p,q)$ network does freeze rather than scale, the exclusion the authors note would apply to a much wider class of models than the ones computed here, since freezing is driven by topology rather than by the detailed tension spectrum.
  • The intercommutation probability being below unity gives an observational handle that is independent of tension, so a joint measurement of $G mu$ and of reconnection statistics would separate fundamental from field-theoretic strings even if the tensions happened to coincide.
Original abstract

Macroscopic fundamental and Dirichlet strings have several potential instabilities: breakage, tachyon decays, and confinement by axion domain walls. We investigate the conditions under which metastable strings can exist, and we find that such strings are present in many models. There are various possibilities, the most notable being a network of (p,q) strings. Cosmic strings give a potentially large window into string physics.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,488 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v5. Results and the main claim are underlined; .

Macroscopic fundamental and Dirichlet strings have several potential instabilities: breakage, tachyon decays, and confinement by axion domain walls. We investigate the conditions under which metastable strings can exist, and we find that such strings are present in many models. There are various possibilities, the most notable being a network of (p,q) strings. Cosmic strings give a potentially large window into string physics.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Macroscopic fundamental and Dirichlet strings have several potential instabilities: breakage, tachyon decays, and confinement by axion domain walls. background 1.00 0.08 0.04 hedged possibility 0.76
s1 We investigate the conditions under which metastable strings can exist, and we find that such strings are present in many models. contribution 0.53 0.96 0.68 asserted 1.00
s2 There are various possibilities, the most notable being a network of (p,q) strings. result 0.73 0.21 0.10 hedged possibility 0.66
s3 Cosmic strings give a potentially large window into string physics. interpretation 0.52 0.12 0.08 hedged possibility 0.89

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.66.

What was examined, and what was not

sources read
  • arXiv listing abstract v5
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. A long open string converts to short open strings on a stringy time scale. quanta as in figure 1. The modern interpretation is that these endpoints are attached to a spacetime-filling D9-brane. Similarly, the fundamental type II string (F-string) can end on any D-brane, and so in any type II model with Dp-branes that fill the noncompact M4 dimensions there will be an amplitude for the string to break. Of course, for p < 9 the D-brane does not fill the compact dimensions, and there is the possibility that the breaking is suppressed due to transverse separation between the string and…
Figure 2. When a string ends on a brane, flux lines in the brane still con￾nect the endpoints. end on a D3-brane [15, 16] and so will be un￾stable in compactifications with D3-branes. A D-string can also end on a D5-brane, but ac￾tually this does not represent an instability. When an F- or D-string ends on a D3-brane, the endpoints are electric or magnetic sources on the brane. The endpoint pair that is pro￾duced when a string breaks are still connected by flux lines in the brane — one can think of the string as dissolving into the brane and becoming flux. For a D-string oriented in the 1-dir
Figure 3. Schematic picture of the KKLMT geometry: a warped Calabi-Yau manifold with throats, identified under a Z2 orientifold. O3-planes.4 The spacetime metric is warped, ds2 = e 2A(x⊥) ηµν dxµ dxν + ds2 ⊥ . (3.1) The inflaton is the separation between a D3-brane and an anti-D3-brane, whose annihilation leads to reheating. The annihilation occurs in a region (throat) of large gravitational redshift, min{e A(x⊥)} = e A0 ≪ 1, where e A(x⊥) is normalized to be O(1) in the bulk of the Calabi-Yau. Note that in figure 3 the covering manifold has two throats which are identified under the Z2
Figure 4. When two strings of the same type cross they can intercommute (reconnect). fundamental bosonic strings the probability was obtained in ref. [40]. The same result holds for the superstring [42]: the probability is of order P ∼ 0.5g 2 s Vmin V (5.4) for a typical collision. Here V is the six-volume within which the strings are confined, and Vmin = (4π 2α ′ ) 3 is the minimum volume for toroidal compactification. For gs > 1 – 17 –
Figure 5. Crossing of strings of different types. produce a (p + p ′ , q + q ′ ) string or a (p − p ′ , q − q ′ ) string.8 Only for (p ′ , q′ ) = ±(p, q) is the usual intercommutation possible. A more complete treatment of this subject is in preparation [42]. 5.1.4 Network properties After their formation at the end of inflation, string networks decay by the com￾bined processes of intercommutation, which breaks longer strings into smaller loops, 8There has been extensive study of two-dimensional supersymmetric networks formed in this way; see for example ref. [41]. – 18 –

Figures reproduced from arXiv:hep-th/0312067 by the authors.

References
How the literature uses it

136 arXiv papers cite this in 186 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 91 sentences without a confident label

Builds on it 1 paper
Compares with it 3 papers
Cites it as background 76 papers
  • In 4-dimensional spacetime, $A_μν$ is dual to an axion $a$ i.e. $∂^μa=ϵ^μνρσ∂_νA_ρσ$.[A realistic compactification from 10 to 4 dimensions in Type IIB string theory possesses an orientifold, in which the original two-forms $B_μν$ and $C_μν$ are projected out [ref] .

    Periodic Fast Radio Bursts from Axion Emission by Cosmic Superstrings · Introduction · 0.91

  • Cosmic strings play a significant part in the study of the early universe: they are characteristic of axionic dark matter, can lead to important effects on baryogenesis [ref] , and commonly arise in string theory models [ref] .

    Revisiting Scattering Enhancement from the Aharonov-Bohm Effect · Introduction · 0.94

  • The subject has been recently regenerated by the progressive realization [ref] that cosmic strings occur also as fundamental objects of string theory, see [ref] for reviews.

    Cosmic Super-Strings and Kaluza-Klein Modes · Introduction · 0.93

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