REVIEW
How generic is cosmic string formation in SUSY GUTs
High Energy Physics - Phenomenology · Submitted 12 Aug 2003 · 67 references
Pith's verdict: The SO(10), E6 and SU(6) enumerations are real work and the conclusion holds there; the rank-7 and rank-8 half of the 'rank 4 to 8' claim is asserted rather than shown, and the 'unavoidable' headline leans harder on the inflation and leptogenesis filters than the abstract lets on.
T0 · AI review
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Referee report
The paper
The paper claims
Sweeping every symmetry-breaking chain from rank-4 to rank-8 unified groups, the authors find that no scheme survives inflation, leptogenesis and proton-decay constraints without leaving cosmic strings behind.
The reading
What carries the argument
The engine is the homotopy classification of defects, applied transition by transition along each chain. For a breaking $G to H$, the vacuum manifold is $G/H$, and the homotopy groups $pi_k(G/H)$ tell you what forms: $pi_0 neq 0$ gives domain walls, $pi_1 neq 0$ gives cosmic strings, $pi_2 neq 0$ gives monopoles, $pi_3 neq 0$ gives textures. Embedded defects are tracked separately by testing $pi_k(G_{emb}/H_{emb})$ for subalgebras, and the paper keeps embedded strings but discards embedded monopoles because they are unstable. Layered on top is the inflationary filter. Standard hybrid inflation with superpotential $W = alpha S Phi bar{Phi} - mu^2 S$ requires the rank of the group to drop by at least one unit, and the symmetry breaking happens in the waterfall at the end of inflation, so any defect associated with that transition is produced after inflation and survives. That immediately kills chains where the rank-lowering step makes monopoles or walls, and it makes string formation at the final rank-lowering step essentially automatic. The third layer is the phenomenology filter: unbroken $Z_2$ (matter parity) for proton stability, and $B-L$ broken at the end of inflation so that non-thermal leptogenesis from inflaton decay, and the decay of $B-L$ strings themselves, can generate the baryon asymmetry.
Extended reading notes
Core claim
The paper's claim is a negative completeness result: there is no acceptable spontaneous symmetry breaking chain from a simple supersymmetric GUT of rank 4 to 8 down to $G_{SM} = SU(3)_C times SU(2)_L times U(1)_Y$ that avoids cosmic string formation after inflation. The counting is explicit. For $SO(10)$ there are 68 chains free of unwanted defects after inflation, of which 34 have topological strings with unbroken matter parity and satisfy every constraint. For $E_6$ broken through $SO(10) times U(1)$, 146 chains survive all filters and all give topological strings; through $SU(3)_C times SU(3)_L times SU(3)_R$, 444 survive; through $SU(6) times SU(2)$, 534 survive. $SU(6)$ and $SU(7)$ are set aside because they lack a gauged $B-L$ and so cannot accommodate neutrino masses through the see-saw, and minimal $SU(5)$ is already excluded by proton lifetime. The authors also record two structural corollaries: the strings formed at the end of inflation have tension proportional to the inflationary scale $mu/sqrt{alpha}$, and for groups of rank above six, where more than one rank-lowering transition occurs, successive short inflationary bursts can take place and a second, lower-scale string network can form.
Load-bearing premise
The conclusion rests on assuming standard hybrid inflation in which the rank-lowering symmetry breaking, and with it the breaking of $B-L$, happens in the waterfall at the end of inflation; the authors are aware of the alternative non-renormalizable superpotential term that would break the GUT during inflation instead, and set it aside.
Editorial extensions
If this is right
- If the conclusion holds, the string tension is not a free parameter: it is fixed by the inflationary scale $mu/sqrt{alpha}$, so any detection or bound on a string contribution to the cosmic microwave background translates directly into a constraint on the inflation scale of these models.
- Cosmological models built on these GUTs should be analysed as mixed scenarios, with the angular power spectrum written as a weighted sum of an inflationary and a string contribution rather than as pure inflation.
- Because the surviving chains have $B-L$ broken at the end of inflation, the strings are $B-L$ strings carrying right-handed neutrino zero modes, so their decays add a second, non-thermal channel to the lepton asymmetry alongside reheating.
- For groups of rank above six, the same framework predicts a sequence of short inflationary bursts at different scales, leaving a distinctive stepped imprint on the scalar perturbation spectrum.
- Groups without a gauged $B-L$, such as minimal $SU(6)$ and $SU(7)$, are excluded on particle-physics grounds before the defect analysis even matters, which narrows the viable unification landscape independently of cosmology.
Reading between the lines
- The result is best read as a statement about the filter, not about the landscape: because the authors require the rank-lowering breaking to occur in the waterfall at the end of inflation, and that step breaks a $U(1)$, non-zero $pi_1$ follows almost by construction. The enumeration's real content is the demonstration that no other constraint forces a chain into a defect-free corner.
- A natural next step the paper leaves open is to ask how large the string contribution actually is in each surviving chain. The weighting depends on the coupling $alpha$, the dimension of the Higgs representation, and the group, so a systematic tabulation would turn the qualitative 'strings are generic' into a quantitative prediction that CMB data could confirm or exclude chain by chain.
- The same homotopy-plus-inflation bookkeeping could be run with a different inflationary completion, for instance the non-renormalizable superpotential term that shifts the inflationary valley so the GUT is already broken during inflation. That variant would be the cleanest way to test whether 'unavoidable' is a property of supersymmetric unification or of the specific hybrid inflation model adopte
- The counting is restricted to maximal regular subgroups and to a maximum rank of 8, with the authors noting that higher-rank groups should reproduce similar patterns. A reader could reasonably ask whether the 'no defect-free survivor' pattern is stable under relaxing that rank cut, since the number of chains grows very fast with rank.
Original abstract
We study cosmic string formation within supersymmetric grand unified theories. We consider gauge groups having a rank between 4 and 8. We examine all possible spontaneous symmetry breaking patterns from the GUT down to the standard model gauge group. Assuming standard hybrid inflation, we select all the models which can solve the GUT monopole problem, lead to baryogenesis after inflation and are consistent with proton lifetime measurements. We conclude that in all acceptable spontaneous symmetry breaking schemes, cosmic string formation is unavoidable. The strings which form at the end of inflation have a mass which is proportional to the inflationary scale. Sometimes, a second network of strings form at a lower scale. Models based on gauge groups which have rank greater than 6 can lead to more than one inflationary era; they all end by cosmic string formation.
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
We study cosmic string formation within supersymmetric grand unified theories. We consider gauge groups having a rank between 4 and 8. We examine all possible spontaneous symmetry breaking patterns from the GUT down to the standard model gauge group. Assuming standard hybrid inflation, we select all the models which can solve the GUT monopole problem, lead to baryogenesis after inflation and are consistent with proton lifetime measurements. We conclude that in all acceptable spontaneous symmetry breaking schemes, cosmic string formation is unavoidable. The strings which form at the end of inflation have a mass which is proportional to the inflationary scale. Sometimes, a second network of strings form at a lower scale. Models based on gauge groups which have rank greater than 6 can lead to more than one inflationary era; they all end by cosmic string formation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study cosmic string formation within supersymmetric grand unified theories. | contribution 0.97 | 0.90 | 0.02 | asserted 0.60 |
| s1 | We consider gauge groups having a rank between 4 and 8. | method 0.61 | 0.61 | 0.01 | asserted 0.86 |
| s2 | We examine all possible spontaneous symmetry breaking patterns from the GUT down to the standard model gauge group. | method 0.68 | 0.89 | 0.02 | asserted 0.76 |
| s3 | Assuming standard hybrid inflation, we select all the models which can solve the GUT monopole problem, lead to baryogenesis after inflation and are consistent with proton lifetime measurements. | method 0.95 | 0.85 | 0.03 | asserted 0.64 |
| s4 | We conclude that in all acceptable spontaneous symmetry breaking schemes, cosmic string formation is unavoidable. | result 0.98 | 0.91 | 0.94 | asserted 1.00 |
| s5 | The strings which form at the end of inflation have a mass which is proportional to the inflationary scale. | result 1.00 | 0.79 | 0.03 | asserted 1.00 |
| s6 | Sometimes, a second network of strings form at a lower scale. | result 1.00 | 0.77 | 0.02 | hedged possibility 0.76 |
| s7 | Models based on gauge groups which have rank greater than 6 can lead to more than one inflationary era; they all end by cosmic string formation. | result 1.00 | 0.83 | 0.11 | asserted 0.63 |
What was examined, and what was not
- arXiv listing abstract v1
- 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
References
How the literature uses it
124 arXiv papers cite this in 144 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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We conclude that all acceptable symmetry breaking schemes produce cosmic strings after the last inflationary phase.
Papers citing it · 79 sentences without a confident label
Compares with it 1 paper
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We like to point out that the class of promising SO(10) models we considered in this work may or may not lead to the formation of CSs, contrary to the class of models considered in [ref] , where the appearance of CSs is unavoidable.
Singling out SO(10) GUT models using recent PTA results · Introduction · 0.97
Cites it as support 2 papers
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It was pointed out that, if we try to embed this model of hybrid inflation into a realistic model of supersymmetric GUT, the formation of cosmic strings is inevitable [ref] .
Supergravity based inflation models: a review · Hybrid inflation · 0.98
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Considering all possible spontaneous symmetry breaking patterns from the GUT down to the SM gauge group, it was shown [ref] that cosmic string formation is unavoidable.
Detection of Early-Universe Gravitational Wave Signatures and Fundamental Physics · Topological Defects · 0.98
Cites it as background 62 papers
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Moreover several Standard Model extensions, such as models of Grand Unified Theory (GUT) [ref] , or the seesaw mechanism for generating the neutrino masses in the Standard Model when $U_B-L(1)$ is broken spontaneously [ref] .
Cosmic string gravitational waves from global $U(1)_{B-L}$ symmetry breaking as a probe of the type I seesaw scale · Gravitational Waves from Global Cosmic Strings · 0.90
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One such alternative is the gravitational collapse of cosmic strings [ref] : 1+1-dimensional topological defects which are generic predictions of many extensions to the Standard Model [ref] .
Primordial black holes from cusp collapse on cosmic strings · Introduction · 0.92
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We consider cosmic strings associated with the spontaneous breaking of a local $U(1)$ symmetry embedded in a grand unified theory (GUT) [ref] , a prominent example being the breaking of $B-L$, the difference of baryon and lepton number [ref] .
Stochastic gravitational-wave background from metastable cosmic strings · Introduction · 0.88
Discussion
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