REVIEW
Supersymmetric Standard Model from the Heterotic String (II)
High Energy Physics - Theory · Submitted 20 Jun 2006 · 103 references
Pith's verdict: The detailed companion to the 2005 Z6-II MSSM letter: explicit shift vectors, Wilson lines, spectrum, flat direction and Yukawa textures — a benchmark construction whose one real soft spot, uncomputed order-one Yukawa coefficients for exotic decoupling, is standard for the field rather than fatal.
T0 · AI review
Why Pith says this
Highlight any text to comment on it.
Referee report
The paper
The paper claims
A specific $Z_6$ orbifold of the heterotic string is claimed to reproduce the supersymmetric Standard Model.
The reading
What carries the argument
The load-bearing objects are the orbifold shift vectors and Wilson lines embedded in $E_8$, which determine the unbroken gauge group, the fixed-point local symmetries, and the matter spectrum. The paper classifies the twisted and untwisted string states by their $Z_6$-II boundary conditions, identifies the three $16$-plets, and computes the allowed Yukawa couplings from string selection rules. A second mechanism is the singlet flat direction: the exotics are lifted by couplings to Standard Model singlet fields whose vacuum expectation values preserve $D$- and $F$-flatness, and the same singlet fields generate the hierarchical Yukawa matrix. Gaugino condensation in the hidden $SU(4)$ sector supplies a route to supersymmetry breaking.
Extended reading notes
Core claim
The central claim is that the $Z_6$-II orbifold of the heterotic $E_8$ string, with shift vectors $V_6$, $W_2$, $W_3$ and Wilson lines $V'_6$, $W'_2$, $W'_3$, breaks the ten-dimensional gauge group to $SU(3)_c$ times $SU(2)_L$ times $U(1)_Y$ times a hidden $SU(4)$ times $SU(2)'$ and extra $U(1)$ factors. The quark and lepton zero modes appear as three $16$-plets of $SO(10)$; two are localized at $T_1$ fixed points that retain a local $SO(10)$ symmetry, while the third sits at $U$, $T_2$, or $T_4$. The paper then exhibits a $D$- and $F$-flat direction in the Standard Model singlet fields along which all exotic states become massive, leaving the MSSM spectrum at low energies. It further shows that the top quark Yukawa coupling comes from gauge interactions and is of order the gauge coupling, while the remaining Yukawa couplings are suppressed by powers of singlet fields in the manner of Froggatt-Nielsen.
Load-bearing premise
The load-bearing premise is that the string selection rules give nonzero order-one coefficients for every coupling needed to lift the exotic states along the proposed singlet flat direction; if any required coupling vanishes, an exotic remains massless and the low-energy spectrum is not the MSSM.
Editorial extensions
If this is right
- The model gives an explicit string-derived MSSM spectrum with gauge coupling unification near $2$ times $10^{16}$ GeV.
- The top quark Yukawa coupling is tied to the gauge coupling, so the observed top mass must come mostly from the ratio of Higgs vacuum expectation values rather than from a free coupling.
- The remaining quark and lepton Yukawa hierarchies follow from powers of Standard Model singlet fields, giving a string realization of the Froggatt-Nielsen pattern.
- Hidden-sector gaugino condensation can break supersymmetry, and the model's large vacuum degeneracy allows vacua with an approximate $B-L$ symmetry.
Reading between the lines
- If this vacuum is realized, the fixed-point local $SO(10)$ symmetry may leave a calculable flavor imprint, making the model distinguishable from generic MSSM fits by correlations among fermion masses and mixings.
- The claim of no light exotics is a sharp prediction of this vacuum: discovery of a light exotic with Standard Model quantum numbers would rule out this compactification, though not the heterotic string more broadly.
- The large vacuum degeneracy suggests that the model's low-energy predictions should be phrased statistically over vacua rather than as a single point, a question the paper leaves for later work.
- The approximate $B-L$ symmetry could be relevant to neutrino masses and proton stability, but the paper does not derive those consequences here.
Original abstract
We desribe in detail a Z_6 orbifold compactification of the heterotic E_8 x E_8 string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three 16-plets of SO(10), two of which are localized at fixed points with local SO(10) symmetry. The model has supersymmetric vacua without exotics at low energies and is consistent with gauge coupling unification. Supersymmetry can be broken via gaugino condensation in the hidden sector. The model has large vacuum degeneracy. Certain vacua with approximate B-L symmetry have attractive phenomenological features. The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings. The other Yukawa couplings are suppressed by powers of standard model singlet fields, similarly to the Froggatt-Nielsen mechanism.
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 desribe in detail a Z_6 orbifold compactification of the heterotic E_8 x E_8 string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three 16-plets of SO(10), two of which are localized at fixed points with local SO(10) symmetry. The model has supersymmetric vacua without exotics at low energies and is consistent with gauge coupling unification. Supersymmetry can be broken via gaugino condensation in the hidden sector. The model has large vacuum degeneracy. Certain vacua with approximate B-L symmetry have attractive phenomenological features. The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings. The other Yukawa couplings are suppressed by powers of standard model singlet fields, similarly to the Froggatt-Nielsen mechanism.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We desribe in detail a Z_6 orbifold compactification of the heterotic E_8 x E_8 string which leads to the (supersymmetric) standard model gauge group and matter content. | contribution 0.99 | 0.94 | 0.74 | asserted 1.00 |
| s1 | The quarks and leptons appear as three 16-plets of SO(10), two of which are localized at fixed points with local SO(10) symmetry. | result 0.87 | 0.84 | 0.12 | asserted 1.00 |
| s2 | The model has supersymmetric vacua without exotics at low energies and is consistent with gauge coupling unification. | result 0.98 | 0.83 | 0.24 | asserted 0.94 |
| s3 | Supersymmetry can be broken via gaugino condensation in the hidden sector. | result 0.60 | 0.48 | 0.05 | hedged possibility 0.97 |
| s4 | The model has large vacuum degeneracy. | result 0.98 | 0.83 | 0.05 | asserted 1.00 |
| s5 | Certain vacua with approximate B-L symmetry have attractive phenomenological features. | result 0.57 | 0.80 | 0.06 | asserted 0.82 |
| s6 | The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings. | result 1.00 | 0.82 | 0.08 | asserted 1.00 |
| s7 | The other Yukawa couplings are suppressed by powers of standard model singlet fields, similarly to the Froggatt-Nielsen mechanism. | result 0.92 | 0.78 | 0.05 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v3
- 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
44 arXiv papers cite this in 69 sentences
Papers citing it · 49 sentences without a confident label
Compares with it 1 paper
-
Froggatt-Nielsen type models have perhaps the most similarity with our mechanism but usually require careful choices of new charges for the different SM quarks and leptons as well as many new fields in order to accommodate the observed hierarchical structure [ref] .
A Domino Theory of Flavor · Flavor Philosophy · 0.96
Cites it as support 1 paper
-
Indeed, such possibility has been examined in explicit models [ref] .
Higher Order Couplings from Heterotic Orbifold Theory · Introduction · 0.96
Cites it as background 16 papers
-
Several approaches have been proposed and used over the years: smooth Calabi-Yau compactifications based on the standard embedding [ref] , non-standard embedding models [ref] , models based on orbifolds [ref] , free fermionic strings [ref] and Gepner models [ref] .
A Comprehensive Scan for Heterotic SU(5) GUT models · Introduction and Summary · 1.00
-
We begin with a brief review of the stringy embedding of orbifold GUTs [ref] , and a presentation of the models in the “mini-landscape" search [ref] in Section [ref].
Reconciling Grand Unification with Strings by Anisotropic Compactifications · Introduction · 1.00
-
In order to clarify certain fine points that have caused us much confusion, we found useful to include in Appendix [ref] a brief review of the string theory construction for the $Z_6-II$ orbifold complementing the detailed discussions in [ref] .
Searching singlet extensions of the supersymmetric standard model in $ Z_{6-II}$ orbifold compactification of heterotic string · Introduction · 0.97
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.