Sequestering in String Theory

Liam McAllister; Raman Sundrum; Shamit Kachru

REVIEW

Sequestering in String Theory

Shamit Kachru, Liam McAllister, Raman Sundrum

High Energy Physics - Theory · Submitted 10 Mar 2007 · 66 references

Pith's verdict: The warped-sequestering result holds up on two independent routes, but the compactification step in §4.3 is argued rather than computed, and the authors say so themselves.

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CitationLiam McAllister, Raman Sundrum, Shamit Kachru. "Sequestering in String Theory." arXiv:hep-th/0703105 (2007). https://pith.science/paper/PUUF2NTT

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Editor's note

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Worth your time, with one caveat the authors flag themselves. The core claim is that warped throats sequester and unwarped compactifications generically don't. Two largely independent arguments land on the same answer: the AdS/CFT operator analysis in §3.2, where the leading dangerous operators are O8 with dimension 8 and O_sqrt28 at about 5.29, and the explicit D3/anti-D3 gravity computation in §4.2, Eq. 4.10, which shows the cross-coupling suppressed by eight powers of the IR warp factor. That agreement is the paper's real strength. The two routes corroborate rather than assume each other, which is more than a lot of the sequestering literature manages. The §2 unwarped analysis is also careful. Eq. 2.23 is derived indirectly, from the Gauss's law constraint on the warp factor, and cross-checked against the explicit Grana-Grimm-Jockers-Louis computation, which is published. The single-modulus case (2.21) is genuinely sequestered; multi-moduli generically isn't. Clean and useful. Where it's soft is §4.3, the step from non-compact throat to compactification. The authors argue by locality that induced couplings must pass through throat modes, and that the dominant ones are the SU(2)xSU(2) KK gauge bosons, harmless by [16]. But §2.3 already concedes that the [31] wavefunction-overlap argument 'is not quite justified.' And the [16] current criterion is a statement about conserved-current bilinears; the overall volume modulus is dual to the dilatation current, which isn't conserved in the confining IR. §2 taught us that Kähler-modulus mixing is exactly what spoils sequestering in the unwarped multi-modulus case, and the paper doesn't show the warped analog is either additive or a conserved-current coupling. The N=4 toroidal orientifold check in §4.3 is a special case with enough supersymmetry to fix the Kähler potential exactly; it doesn't test the generic warped case. This is a real gap, not a fatal one. The warp-factor suppression is robust enough that I expect the conclusion survives, but it's argued, not computed. Second, milder: the reliance on [16] is conditional on the hidden sector preserving the relevant symmetry near the supersymmetry-breaking scale. The paper checks this for the conifold and doesn't establish it in general. Who should read it: anyone working on anomaly mediation, mirage mediation, or warped model building. It's the standard reference for warped sequestering and it earns that status. Send it out.

Referee report

Major objections (1)

[§4.3, and the transition from §4.2 to §4.3] The compactification step is the weakest link in the argument that warped compactifications 'readily sequester' (abstract:s1). The non-compact throat computation of Eq. (4.10) and the AdS/CFT operator analysis of §3.2 both establish suppression by the IR warp factor in the non-compact throat. The step that carries this into a genuine compactification is the locality argument of §4.3: any compactification-induced coupling between a UV brane and an IR brane must propagate through throat modes, and the dominant unsuppressed modes are the SU(2)xSU(2) KK gauge bosons, which are dual to conserved currents and harmless by [16]. Two gaps remain. First, the paper itself states in §2.3 that the [31] argument — that the bulk Kähler modulus wavefunction has negligible overlap with the tip — 'is not quite justified.' Second, the fallback to [16] is a statement about conserved-current bilinears in the hidden sector; the overall volume modulus is dual to the dilatation current, which is not conserved in the confining IR, so [16] does not obviously neutralize a volume-modulus coupling to the tip brane. §2 showed that in the unwarped multi-modulus case it is precisely Kähler-modulus mixing (Eq. 2.23) that spoils sequestering; the paper does not demonstrate that the warped analog of that mixing is either additive (as in the single-modulus Eq. 2.21) or a conserved-current coupling. The N=4 toroidal orientifold check in §4.3 is a special case with enough supersymmetry to fix the Kähler potential exactly and does not test the generic warped case. I would ask the authors either to compute the volume-modulus coupling to a tip-localized brane in a warped compactification, or to give a sharper argument for why the locality argument covers the volume modulus. This does not undermine the non-compact results, but it is needed for the compactification claim.

Minor objections (6)

[Abstract] The phrase 'readily sequester' is a little strong given the §4.3 caveat; it would be more accurate to say that the suppression is established in the non-compact throat and argued by locality in the compact case.
[§3.2 and §4.2] §3.2 states that O8 transmits soft terms suppressed by (Λ_IR/Λ_UV)^4, while §4.2 states that the cross-coupling is suppressed by eight powers of the IR warp factor. These are consistent if the former is relative to dimension-2 bilinears and the latter is absolute, but the paper does not say so explicitly; a clarifying sentence would help the reader.
[§4.3] The claim that the dominant unsuppressed modes are the SU(2)xSU(2) KK gauge bosons is asserted rather than justified; a sentence explaining why these modes dominate over other throat KK modes would strengthen the argument.
[§5] The claim that the non-Abelian orbifold CFTs 'provide a counterexample to the expectation in [37]' is somewhat strong, since 'typical' is doing work in that expectation; the authors might hedge this to 'an exception' rather than 'a counterexample.'
[Eqs. (2.16)-(2.17)] The normalization ∫_Σ sqrt(g̃) = 1 is a choice; a sentence noting that the physical results are independent of this normalization would help.
[Reference [55]] Reference [55] is listed as 'work in progress'; it is used only for a forward-looking remark and not to support any result, so this is acceptable, but the authors might note that no claim depends on it.

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The paper

The paper claims

The paper argues that strongly warped throats suppress the cross-coupling between a hidden supersymmetry-breaking sector and visible matter, while unwarped compactifications regenerate it through Kähler moduli.

The reading

The paper asks whether string theory can keep a hidden sector that breaks supersymmetry from talking directly to the visible-sector squarks and sleptons. Such a direct coupling, written in curved superspace as $d^4θ X^†X c_{ij} Q_i^†Q_j/M_P^2$, would generate flavor-violating soft masses and spoil anomaly mediation, gaugino mediation, and mirage mediation. The authors argue that the answer turns on warping: in ordinary unwarped compactifications the coupling is generically regenerated, because the positions of D3-branes mix into the Kähler moduli that measure the size of the compact space. In strongly warped throats of the Klebanov-Strassler type the coupling is instead suppressed by powers of the infrared warp factor, and the AdS/CFT dual of that suppression is conformal sequestering. If the argument holds, a compactification of the KKLT type can host flavor-blind supersymmetry breaking without extra model building.

What carries the argument

Two mechanisms carry the argument. The first is moduli mixing: because the compact space is finite, a D3-brane's position $x$ shifts the local warp factor by an amount fixed by Gauss's law, $g̃^{ij̄}∂_i∂_{j̄}δh = (T_3/M_P^2)e^{-4u}$, and that shift is absorbed into the holomorphic Kähler coordinates $T_α$. Whether the resulting $f$ is sequestered then reduces to whether the $x$-dependence enters additively, which happens for one modulus and fails for several. The second is the AdS/CFT reading of a warped throat: the throat is dual to a strongly coupled CFT with a cascade of Seiberg dualities, and sequestering becomes conformal sequestering, in which a hidden operator of dimension $2+Δ$ suppresses the naive cross-coupling by $(Λ_{IR}/Λ_{UV})^Δ$. The Kaluza-Klein spectrum on $T^{1,1}$ then fixes which operators can mediate; the conserved $SU(2)×SU(2)$ currents are harmless under the milder criterion of Schmaltz and Sundrum, since a conserved Noether current has no supersymmetry-breaking vacuum expectation value.

Extended reading notes

Core claim

Sequestering means that the coefficient $c_{ij}$ in the curved-superspace cross term $d^4θ X^†X c_{ij}(Q^i)^†Q^j/M_P^2$ is much less than one, where $X$ carries the dominant $F$-term and $Q$ are the visible chiral fields; the cross term that matters is the one in $f = -3M_P^2 exp(-K/3M_P^2)$, not in $K$ itself. The paper's central claim is that warped compactifications of type IIB string theory deliver this suppression robustly while unwarped ones generically do not. In the unwarped case the authors show that the warp-factor perturbation sourced by one D3-brane stack obeys $∂_i∂_{j̄}δh = (T_3/3M_P^2)e^{-4u} g̃_{ij̄}$, so the holomorphic four-cycle volume becomes $T_α + T̄_α - γk_α(x,x̄) - γk_α(x',x̄')$; with a single Kähler modulus the brane dependences enter $f$ additively and sequestering survives, while with several moduli it does not. In a Klebanov-Strassler throat the leading operators available to transmit breaking are the $SU(2)×SU(2)$-invariant $O_8 = W^{2α}W^2_{α̇}$ with highest component of dimension 8, or $O_{√28}$ of dimension about 5.29 when the breaking picks out a $(3,3)$ direction. The gravity-side check is the D3/anti-D3 potential $V(r_{UV}) = 2T_3 (r_0/R)^4 (1 - N^{-1} r_0^4/r_{UV}^4)$, whose cross term carries eight powers of the infrared warp factor, matching the dimension-8 operator.

Load-bearing premise

The load-bearing premise is locality after compactification: that once a throat is glued into a compact Calabi-Yau, any coupling induced between an ultraviolet brane and an infrared brane must still travel through throat modes and so inherits the suppression computed in the non-compact throat, a step the authors argue rather than compute, noting that the full warped Kähler potential has proved elusive.

Editorial extensions

If this is right

Anomaly mediation, gaugino mediation, and mirage mediation become viable inside a KKLT compactification, since the gravity-mediated flavor violation they must beat is suppressed by the throat.
Sequestering survives generic visible-sector model building in the bulk of the Calabi-Yau, including D7-brane constructions, because the suppression is a property of the throat rather than of the visible sector.
The size of the effect is set by the warp factor $r_0/R = exp(-2πK/3g_sM)$, so a modestly long cascade already pushes soft masses below the anomaly-mediated floor.
Throats with less global symmetry than the conifold, such as non-abelian orbifolds preserving only $U(1)_R$, are preferable because fewer conserved currents need to be checked against the milder criterion.

Reading between the lines

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

The additive-versus-multiplicative test in $f$ should apply to other moduli as well, so one can ask whether a compactification with many Kähler moduli but a strong hierarchy of four-cycle volumes is sequestered to a controlled approximation, as the paper's blow-up-mode discussion suggests.
If sequestering is really a statement about the dimension of the lightest non-chiral operator in the hidden CFT, the suppression factor becomes a calculable number once the dual CFT is identified, which would make the soft-mass spectrum of a given throat a prediction rather than a choice.
The argument leans on the milder criterion for conserved currents; a hidden sector whose supersymmetry breaking also breaks the throat's isometries falls back on $O_{√28}$ with dimension about 5.29, giving a suppression of $(Λ_{IR}/Λ_{UV})^{1.29}$ that is weaker but still large for a long cascade.
Because the suppression is a property of the infrared end of the throat, the same logic should transfer to warped constructions in type IIA or eleven dimensions, provided an analogous dual CFT controls the cascade.

Original abstract

We study sequestering, a prerequisite for flavor-blind supersymmetry breaking in several high-scale mediation mechanisms, in compactifications of type IIB string theory. We find that although sequestering is typically absent in unwarped backgrounds, strongly warped compactifications do readily sequester. The AdS/CFT dual description in terms of conformal sequestering plays an important role in our analysis, and we establish how sequestering works both on the gravity side and on the gauge theory side. We pay special attention to subtle compactification effects that can disrupt sequestering. Our result is a step toward realizing an appealing pattern of soft terms in a KKLT compactification.

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, 4,242 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.71 · human participants 0.01 · controlled comparison 0.16 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.59 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We study sequestering, a prerequisite for flavor-blind supersymmetry breaking in several high-scale mediation mechanisms, in compactifications of type IIB string theory. We find that although sequestering is typically absent in unwarped backgrounds, strongly warped compactifications do readily sequester. The AdS/CFT dual description in terms of conformal sequestering plays an important role in our analysis, and we establish how sequestering works both on the gravity side and on the gauge theory side. We pay special attention to subtle compactification effects that can disrupt sequestering. Our result is a step toward realizing an appealing pattern of soft terms in a KKLT compactification.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study sequestering, a prerequisite for flavor-blind supersymmetry breaking in several high-scale mediation mechanisms, in compactifications of type IIB string theory.	contribution 0.72	0.76	0.05	asserted 0.68
s1	We find that although sequestering is typically absent in unwarped backgrounds, strongly warped compactifications do readily sequester.	result 1.00	0.95	0.72	asserted 1.00
s2	The AdS/CFT dual description in terms of conformal sequestering plays an important role in our analysis, and we establish how sequestering works both on the gravity side and on the gauge theory side.	method 0.69	0.86	0.11	asserted 1.00
s3	We pay special attention to subtle compactification effects that can disrupt sequestering.	contribution 0.77	0.68	0.04	unclear 0.45
s4	Our result is a step toward realizing an appealing pattern of soft terms in a KKLT compactification.	interpretation 0.91	0.74	0.18	asserted 0.73

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

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sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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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

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Forward citations

Cited by 13 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Carving Out the Space of 4D CFTs
hep-th 2011-09 accept novelty 8.0 of 10

A semidefinite-programming reformulation of the 4D conformal bootstrap yields substantially stronger bounds on operator dimensions, OPE coefficients, central charges and current normalizations, including a bound on di...
Reflections on Parity Breaking
hep-th 2022-11 accept novelty 7.0 of 10

Spontaneous breaking of a gauged parity symmetry gives exactly stable domain walls, because no parity vortex can exist: every closed loop is orientable.
Monodromy in the CMB: Gravity Waves and String Inflation
hep-th 2008-03 conditional novelty 7.0 of 10

Monodromy of a D4-brane on a Nil manifold yields a phi^(2/3) inflaton potential, predicting ns around 0.98 and r around 0.04, a testable gravitational-wave signature from string theory.
de Sitter Vacua from Ten Dimensions
hep-th 2019-08 conditional novelty 6.0 of 10

Gaugino condensation on D7-branes plus anti-D3-branes produce a ten-dimensional stress-energy that exactly reproduces the KKLT four-dimensional scalar potential and curvature.
Fine Tuning, Sequestering, and the Swampland
hep-th 2019-05 conditional novelty 6.0 of 10

Any effective field theory coupled to gravity admits only finitely many fine-tunable parameters, so almost all conformal field theories cannot be consistently coupled to gravity and belong to the swampland.

Show 8 more citing papers

Planck-Suppressed Operators
hep-th 2013-04 conditional novelty 6.0 of 10

Planck non-Gaussianity limits require any dimension-five coupling between a shift-symmetric inflaton and a light hidden sector to be suppressed by at least 10^2 to 10^5 Hubble scales, depending on the hidden sector's ...
Simply Unnatural Supersymmetry
hep-ph 2012-12 conditional novelty 6.0 of 10

Split supersymmetry with scalars at 100-1000 TeV and TeV-scale gauginos fits the 125 GeV Higgs mass, gauge coupling unification, and wino dark matter, and predicts distinctive displaced gluino decays.
Sequestering in String Compactifications
hep-th 2010-12 conditional novelty 6.0 of 10

Nonperturbative moduli stabilization in type IIB string theory generically induces visible-hidden superpotential couplings that spoil sequestering, giving Higgs Bmu terms of order the gravitino mass and, in the Large ...
Holographic Gauge Mediation
hep-th 2009-03 conditional novelty 6.0 of 10

In a warped conifold with anti-D3 branes and Kuperstein D7-branes, the leading Standard Model gaugino mass arises from one-loop splittings of adjoint messenger mesons, scaling as (S/mu^2) times a tower sum.
Holographic Systematics of D-brane Inflation
hep-th 2008-08 conditional novelty 6.0 of 10

Bulk-induced corrections to the D3-brane inflaton potential in the warped deformed conifold are classified by the dimension of the dual CFT operator, yielding either a phi^{3/2} inflection term or a negative mass-squa...
Dynamics of Warped Flux Compactifications
hep-th 2008-03 conditional novelty 6.0 of 10

Warp corrections to the four-dimensional effective action of type IIB flux compactifications leave kinetic terms diagonal in a warped KK basis and modify the complex structure Kähler potential relative to prior proposals.
A Gravity Dual of Metastable Dynamical Supersymmetry Breaking
hep-th 2008-01 conditional novelty 6.0 of 10

A linearized ten-dimensional supergravity solution describes the backreaction of anti-D3-branes at the tip of the Klebanov-Strassler throat, yielding a nonzero energy density and operator vacuum expectation values in ...
The $G_2$-MSSM - An $M$ Theory motivated model of Particle Physics
hep-ph 2008-01 conditional novelty 6.0 of 10

Within the authors' G2 compactification framework, gaugino masses are suppressed by a factor of about 83 relative to the gravitino, giving heavy multi-TeV scalars, sub-TeV gauginos, and a wino-like lightest superpartner.

How the literature uses it

49 arXiv papers cite this in 85 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 · 64 sentences without a confident label

Contests it 1 paper

Thus, in KKLT compactifications, the sequestering described in [ref] does not survive moduli stabilization.

Sequestering in String Compactifications · Conclusions · contest 0.76

Builds on it 2 papers

In this paper, we have studied in some more detail how the mechanism of mild sequestering proposed in [ref] may be technically realized in supergravity and string models.

Mildly sequestered supergravity models and their realization in string theory · Conclusions · 0.85
In this Appendix we show that warped sequestering in the no-scale setup of [ref] survives the relaxation of an assumption made for technical simplicity in [ref] : smearing of the supersymmetry-breaking anti-D3-brane around the $S^3$ tip of the warped deformed conifold is not required for the basic conclusion to hold.

Sequestering in String Compactifications · Smeared Sources and Warped Sequestering · 0.81

Compares with it 1 paper

Therefore, supersymmetry breaking in this model does not sequester, in contrast to the positive result obtained by [ref] for the corresponding configuration before Kähler moduli stabilization.

Sequestering in String Compactifications · Conclusions · 0.91

Cites it as support 3 papers

The results of [ref] ensure that higher-order terms in the expansion of the brane-antibrane potential are negligible.

Sequestering in String Compactifications · Soft masses for the D3-brane · 0.97
Such sequestering is known to arise readily in string theory in the presence of strongly warped backgrounds [ref] .

The Goldstini Variations · Warped and Sequestered Goldstini · 0.97
Furthermore, attempts to suppress them completely in UV complete models appear hard, if not impossible [ref] .

Aspects of Modular Flavor Symmetries · Problems with kinetic terms · 0.98

Cites it as background 12 papers

Let us briefly review and clarify the results of [ref] , which analyzed the mediation of supersymmetry breaking from an anti-D3-brane to a D3-brane by normalizable profiles of the supergravity fields in a Klebanov-Strassler throat region of a no-scale compactification.

Sequestering in String Compactifications · Warped sequestering in the Klebanov-Strassler throat · 0.83
See Ref. [ref] for related discussion of this point.

Anomaly-Mediation and Sequestering from a Higher-Dimensional viewpoint · 4D Effective Theory and Sequestering · 0.88
As discussed in [ref] , localized sources involved in moduli stabilization often lead to order one contributions to slow-roll parameters, some of which are rather subtle.

Monodromy in the CMB: Gravity Waves and String Inflation · Contributions to $V,ϵ$, and $η$ from Moduli-Stabilizing Ingredients · 0.84

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.

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