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Soft SUSY Breaking Terms for Chiral Matter in IIB String Compactifications

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Joseph P. Conlon, Shehu S. Abdussalam, Fernando Quevedo, Kerim Suruliz

High Energy Physics - Theory · Submitted 11 Oct 2006 · 60 references

Pith's verdict: Solid application paper: chiral D7 soft terms in the large-volume scenario reduce to a dilaton-domination-like pattern, with a good universality argument; the soft spots are acknowledged limitations and a sign typo, not physics errors.

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arXiv IDhep-th/0610129 (version 2)
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CitationFernando Quevedo, Joseph P. Conlon, Kerim Suruliz, Shehu S. AbdusSalam. "Soft SUSY Breaking Terms for Chiral Matter in IIB String Compactifications." arXiv:hep-th/0610129 (2006). https://pith.science/paper/GD7UKPDB
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The paper

The paper claims

Using newly computed Kähler metrics for chiral D7 matter, the paper derives the soft supersymmetry-breaking terms in IIB flux compactifications and finds they collapse to a one-parameter form set by each field's modular weight.

The reading

The paper asks what supersymmetry breaking looks like for the matter fields that actually make up squarks and sleptons — chiral fields living on magnetised D7 branes — in a IIB Calabi-Yau flux compactification where all moduli are stabilised. The obstacle has always been that the matter Kähler metric for chiral bifundamental fields was unknown, so earlier soft-term studies had to use the metrics for non-chiral adjoint matter. Taking the chiral metrics computed in a companion paper, the authors find that once the metric scales with the large cycle as $p=1$, the F-term of the large modulus cancels out of the soft terms entirely, leaving only the hierarchically smaller F-term of the small cycle. The resulting soft terms are $M_i = F^s/(2T_s)$, $m_alpha = sqrt(lambda), M_i$, $A = -3 lambda M_i$ and $B = -(lambda+1) M_i$, where $lambda$ is the modular weight; for the minimal geometry $lambda = 1/3$ this reproduces the long-studied dilaton-dominated spectrum. The paper then argues that flavour universality is not an accident but a structural feature of IIB flux models, since flavour lives in the complex structure moduli while supersymmetry breaking lives in the Kähler moduli, and the two sectors are block-diagonal in the leading Kähler potential.

What carries the argument

The load-bearing object is the chiral matter Kähler metric $tilde{K}_{alpha beta} = tau_s^lambda V^{2/3} k_{alpha beta}(phi)$, imported from the companion paper and used in the standard supergravity soft-term formulae. Its two features do all the work: the power of the large volume is exactly $p = 1$, which triggers a no-scale cancellation that removes $F^b$ from every soft term, and the residual dependence on the small cycle is a single flavour-universal power $lambda$ multiplying a flavour-dependent function of the complex structure moduli. Because the Kähler moduli cannot appear in the perturbative superpotential (shift symmetry plus holomorphy), $F^m partial_m Y_{alpha beta gamma} = 0$, and because the moduli metric is block-diagonal between Kähler and complex structure sectors, the supersymmetry-breaking sector and the flavour sector never talk at leading order. That decoupling is the mechanism behind the universality claim, and the explicit diagonal and non-diagonal computations are presented as its illustration.

Extended reading notes

Core claim

The central claim is that for chiral D7 matter in the large-volume scenario the soft supersymmetry-breaking terms take the closed form $M_i = F^s/(2T_s)$, $m_alpha = sqrt(lambda) M_i$, $A_{alpha beta gamma} = -3 lambda M_i$ and $B = -(lambda + 1) M_i$, with all dependence on the large cycle cancelling at $p = 1$. For the minimal configuration, where Standard Model branes wrap a single small blow-up cycle with $lambda = 1/3$, this gives $m_alpha = M_i/sqrt(3)$, $A = -M_i$ and $B = -4M_i/3$ — numerically the same pattern as dilaton domination in heterotic models, though arrived at from a completely different microscopic origin. Because every soft term is proportional to $F^s/(2T_s) ~ m_{3/2}/ln(M_P/m_{3/2})$, all of them sit roughly a factor of thirty below the gravitino mass, and the anomaly-mediated contributions, being suppressed both by a loop factor and by the same no-scale cancellation, stay subdominant rather than competing. The paper extends the same computation to arbitrary non-diagonal matter metrics and obtains identical physical results, because the unnormalised soft masses come out proportional to the matter metric itself and the A-terms proportional to the Yukawa couplings. It also notes that the phases of $A/Y$ and of $B$ align with the gaugino phase, so no new CP-violating phases are introduced.

Load-bearing premise

Everything rests on the matter metric scaling as $tilde{K} = tau_s^lambda V^{2/3} k(phi)$ with the large-volume power exactly $p = 1$ and $lambda = 1/3$, a result taken from the companion paper rather than re-derived here; if that power is anything other than one, the cancellation fails and the scalar masses revert to order the gravitino mass.

Editorial extensions

If this is right

  • In the minimal large-volume model the low-energy spectrum is essentially the dilaton-dominated one, with scalars near $M_i/sqrt{3}$ and gauginos near $M_i$, so existing collider studies of that scenario transfer over with the string scale now derived rather than assumed.
  • Because all soft masses scale as $m_{3/2}/ln(M_P/m_{3/2})$, the gravitino can be an order of magnitude or more heavier than the squarks and gauginos without fine-tuning the flux superpotential.
  • Flavour-changing neutral currents from gravity mediation are suppressed at leading order, with the breaking of universality pushed to subleading order in the small-cycle expansion — that is, to loop order in the gauge coupling.
  • Anomaly mediation does not rescue or destabilise the spectrum: its contribution is $g^2/(16 pi^2)$ times an already logarithmically suppressed term, so it can be neglected in spectrum calculations.
  • Running the boundary conditions to the weak scale leaves a viable region for $mu > 0$ with a neutralino LSP satisfying $b to s gamma$, $(g-2)_mu$, Higgs-mass and relic-density bounds, but the high-scale relation $B = -4M/3$ cannot be satisfied there and requires some additional mechanism to generate the correct $B$ term.

Reading between the lines

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

  • If the same scaling argument applies to D3-brane matter in KKLT-type constructions, the no-scale cancellation should suppress anomaly mediation there too, which would undercut the mirage-mediation reading of the one-modulus case; the paper gestures at this but does not carry it out.
  • The prediction that universality breaks first at subleading order in $tau_s$ — i.e. at loop order — gives a sharp target: a computation of the one-loop correction to the matter metric would translate directly into a predicted size for flavour-violating squark mass insertions.
  • Because the soft terms depend on $lambda$ only through a square root and a linear factor, a modest shift in the modular weight (say from $1/3$ toward $1/2$) would move the scalar-to-gaugino mass ratio measurably while leaving the A-term pattern intact, so the spectrum is a more sensitive probe of $lambda$ than the trilinears are.
  • The stated failure to satisfy $B = -4M/3$ alongside the Higgs mass bound suggests the large-volume scenario needs an extension of the Higgs sector or a singlet coupling; the required size of that correction is a concrete model-building question the paper leaves open.
Original abstract

This paper develops the computation of soft supersymmetry breaking terms for chiral D7 matter fields in IIB Calabi-Yau flux compactifications with stabilised moduli. We determine explicit expressions for soft terms for the single-modulus KKLT scenario and the multiple-moduli large volume scenario. In particular we use the chiral matter metrics for Calabi-Yau backgrounds recently computed in hep-th/0609180. These differ from the better understood metrics for non-chiral matter and therefore give a different structure of soft terms. The soft terms take a simple form depending explicitly on the modular weights of the corresponding matter fields. For the large-volume case we find that in the simplest D7 brane configuration, scalar masses, gaugino masses and A-terms are very similar to the dilaton-dominated scenario. Although all soft masses are suppressed by ln(M_P/m_{3/2}) compared to the gravitino mass, the anomaly-mediated contributions do not compete, being doubly suppressed and thus subdominant to the gravity-mediated tree-level terms. Soft terms are flavour-universal to leading order in an expansion in inverse Kahler moduli. They also do not introduce extra CP violating phases to the effective action. We argue that soft term flavour universality should be a property of the large-volume compactifications, and more generally IIB flux models, in which flavour is determined by the complex structure moduli while supersymmetry is broken by the Kahler moduli. For the simplest large-volume case we run the soft terms to low energies and present some sample spectra and a basic phenomenological analysis.

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, 8,284 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.47 · human participants 0.01 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.22 · compares with prior results 0.87 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

This paper develops the computation of soft supersymmetry breaking terms for chiral D7 matter fields in IIB Calabi-Yau flux compactifications with stabilised moduli. We determine explicit expressions for soft terms for the single-modulus KKLT scenario and the multiple-moduli large volume scenario. In particular we use the chiral matter metrics for Calabi-Yau backgrounds recently computed in hep-th/0609180. These differ from the better understood metrics for non-chiral matter and therefore give a different structure of soft terms. The soft terms take a simple form depending explicitly on the modular weights of the corresponding matter fields. For the large-volume case we find that in the simplest D7 brane configuration, scalar masses, gaugino masses and A-terms are very similar to the dilaton-dominated scenario. Although all soft masses are suppressed by ln(M_P/m_{3/2}) compared to the gravitino mass, the anomaly-mediated contributions do not compete, being doubly suppressed and thus subdominant to the gravity-mediated tree-level terms. Soft terms are flavour-universal to leading order in an expansion in inverse Kahler moduli. They also do not introduce extra CP violating phases to the effective action. We argue that soft term flavour universality should be a property of the large-volume compactifications, and more generally IIB flux models, in which flavour is determined by the complex structure moduli while supersymmetry is broken by the Kahler moduli. For the simplest large-volume case we run the soft terms to low energies and present some sample spectra and a basic phenomenological analysis.

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 This paper develops the computation of soft supersymmetry breaking terms for chiral D7 matter fields in IIB Calabi-Yau flux compactifications with stabilised moduli. contribution 1.00 0.93 0.10 asserted 1.00
s1 We determine explicit expressions for soft terms for the single-modulus KKLT scenario and the multiple-moduli large volume scenario. contribution 0.66 0.97 0.16 asserted 1.00
s2 In particular we use the chiral matter metrics for Calabi-Yau backgrounds recently computed in hep-th/0609180. method 0.88 0.34 0.03 asserted 0.99
s3 These differ from the better understood metrics for non-chiral matter and therefore give a different structure of soft terms. background 0.38 0.22 0.06 asserted 1.00
s4 The soft terms take a simple form depending explicitly on the modular weights of the corresponding matter fields. result 1.00 0.88 0.15 asserted 1.00
s5 For the large-volume case we find that in the simplest D7 brane configuration, scalar masses, gaugino masses and A-terms are very similar to the dilaton-dominated scenario. result 1.00 0.96 0.15 asserted 1.00
s6 Although all soft masses are suppressed by ln(M_P/m_{3/2}) compared to the gravitino mass, the anomaly-mediated contributions do not compete, being doubly suppressed and thus subdominant to the gravity-mediated tree-level terms. result 0.98 0.92 0.11 asserted 1.00
s7 Soft terms are flavour-universal to leading order in an expansion in inverse Kahler moduli. result 1.00 0.90 0.17 asserted 1.00
s8 They also do not introduce extra CP violating phases to the effective action. result 1.00 0.84 0.05 asserted 1.00
s9 We argue that soft term flavour universality should be a property of the large-volume compactifications, and more generally IIB flux models, in which flavour is determined by the complex structure moduli while supersymmetry is broken by the Kahler moduli. interpretation 1.00 0.58 0.42 hedged possibility 0.51
s10 For the simplest large-volume case we run the soft terms to low energies and present some sample spectra and a basic phenomenological analysis. contribution 0.89 0.96 0.06 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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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. The physical picture: Standard Model matter is supported on a small blow-up cycle located within the bulk of a very large Calabi-Yau. The volume of the Calabi-Yau sets the gravitino mass and is responsible for the weak/Planck hierarchy. of the small cycles are τs ∼ ln V. For V ∼ 1015 , 4 D7-branes wrapped on such cycles have gauge couplings qualitatively similar to those of the Standard Model. If the branes are magnetised, Standard Model chiral matter can arise from strings stretching between stacks of D7 branes. We assume the Standard Model arises from a stack of magnetised branes w
Figure 2. In the minimal geometry, there is only one small 4-cycle. The different brane stacks of the Standard Model are distinguished by having different magnetic fluxes on the internal 2-cycles of the 4-cycle. In the minimal model above, these 2-cycles are not inherited from the Calabi-Yau and only exist as cycles in the geometry of the 4-cycle. Four distinct brane stacks are required to realise the Standard Model, and we schematically show how these stacks are distinguished by different choices of magnetic flux. in units of MP = 1. Therefore if (as will occur) the dependence of the soft…
Figure 3. Contour plots of (a) BR(b → sγ) (b) δaµ and (c) Ωh 2 on tan β and M, for µ > 0 and ms ∼ 1011 GeV. 2σ bounds are used. The blue region in (d) denotes that the LSP is stau, the white that it is neutralino. bution to dark matter. Since there may be other dark matter constituents, such as axions or for the large volume models the volume modulus, the upper bound on Ωh 2 is the most relevant. The values of the Standard Model input parameters used in our computations are the current central values: mt = 171.4GeV [43], mb(mb)MS = 4.25GeV, αs(MZ ) = 0.1187, α −1 (MZ )MS = 127.918, MZ = 91
Figure 4. Contour plots of (a) BR(b → sγ) (b) δaµ and (c) Ωh 2 on tan β and M for µ < 0 and ms ∼ 1011 GeV. Note that 3σ bounds are used. The blue region in (d) denotes that the LSP is stau, the white that it is neutralino. Figures 3, 4 also show regions in the M − tan β plane with stau LSP. The existence of a stable charged LSP is experimentally ruled out [45] and therefore if such a scenario is to be considered, it must include R parity violation to allow the LSPs to decay before nucleosynthesis. We also scanned the M − tan β parameter space for potentially dangerous charge and colour breakin
Figure 5. Experimental constraints on the parameter space: If a neutralino LSP is to account for the CDM part of the Universe, then the allowed regions 0.085 < Ωχ˜ 0 1 h 2 < 0.125 for (left) µ > 0 and 0.075 < Ωχ˜ 0 1 h 2 < 0.135 for (right) µ < 0 are bounded by the red contours. The bounds are at 2σ and 3σ respectively. The white region represents non neutralino (stau) LSP points. The blue and pink curves respectively are the δaµ and BR(b → sγ) bounds. The cyan curve is the 111 GeV bound on the Higgs mass. The combined results involving all the experimental constraints and displaying stau LSP…
Figure 6. Contour plots of δaµ, BR(b → sγ) and Ωh 2 on tan β and M for (a) µ > 0 and (b) µ < 0 and ms ∼ 1011 GeV. 2σ bounds are used for µ > 0 while 3σ ones are used for µ < 0. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 5 10 15 20 25 30 35 40 45 50 -3B/(4M) tan β M=300GeV M=700GeV M=1100GeV 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 5 10 15 20 25 30 35 40 45 50 -3B/(4M) tan β M=300GeV M=700GeV M=1100GeV (a) (b)
Figure 7. The ratio B/(−4M/3) over a range of values of tan β for (a) µ > 0 and (b) µ < 0 and ms ∼ 1011 GeV. gauge couplings. A further caveat is that there may be additional vector-like matter at the TeV scale that will alter the running of the soft terms (for explicit string models where this effect has been studied see [47]). The results are therefore necessarily approximate and there is a certain amount of ‘theoretical error’ in the soft terms used.9 In particular, we 9 In order to estimate the changes that our assumptions may have, we also computed the spectrum for – 29 –
Figure 8. Pictorial representation of sample mass spectra in allowed µ > 0 region. The numerical values are shown in column B of the sample spectra table. 5. The Simplest KKLT Scenario Let us now briefly recall the one-modulus KKLT scenario. In this case there is only one T field and the volume is given by V = (T + T ∗ ) 3/2 . Here the flux superpotential is required to be very small, W0 ∼ 10−13, in order to address the hierarchy problem. The minimum of the scalar potential is supersymmetric AdS and supersymmetry is only broken by the lifting term, which unfortunately is the least understood
Figure 9. Pictorial representation for sample mass spectra in µ < 0 and stau LSP region. The numerical values are shown in column C of the sample spectra table. non-chiral D7 adjoint matter. The expression for soft masses found in [15] takes the form: m2 λ = (1 − nλ)

Figures reproduced from arXiv:hep-th/0610129 by the authors.

References
How later papers used it

49 later papers cite it

Evidence: some. 34 of the citing papers share no author with it, and 3 of those carry a confident label from Pith's citation classifier.

Pith read 18 of the 116 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its data or values 1 of 2 papers with this label
How the literature uses it

47 arXiv papers cite this in 113 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 · 89 sentences without a confident label

Builds on it 1 paper
  • The purpose of the present paper is to provide a systematic study of the necessary conditions for flavour universal soft terms and it extends arguments made in embryonic form in [ref] (also see [ref] ).

    Mirror Mediation · Introduction · 0.92

Uses its method or tool 1 paper
Uses its data or values 2 papers
Compares with it 3 papers
  • Therefore, by accident, the two terms in the equation above are of the same order which is in contrast to the relation $m_0^gravity= m_1/2^gravity/√(3)$ obtained in the LVS [ref] .

    String GUT Scenarios with Stabilised Moduli · Model 3: An LVS like Supergravity Mediated Model · 0.95

  • Although not our emphasis in this study, the observables used are mostly chosen to be those in [ref] .[The results given for the large-volume models in [ref] differ from those here as the soft terms used are different: in [ref] it was shown that a cancellation exists in the scalar soft terms that significantly reduced the scalar soft terms by a factor $ln(M_P/m_3/2)$ compared to the original estimate of [ref] that was used in [ref] .

    Sparticle Spectra and LHC Signatures for Large Volume String Compactifications · Collider Model and Data Generation · 0.89

  • Since here the phenomenologically relevant sizes of the D7-brane cycles are fixed by the D-term constraints instead of the F-terms, the resulting soft-terms and low-energy signatures are expected to be different from the ones computed so far in the literature for the LARGE volume scenario [ref] .

    GUTs in Type IIB Orientifold Compactifications · Comments on Moduli Stabilisation · 0.99

Cites it as support 1 paper
Cites it as background 14 papers

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