Eleven-Dimensional Supergravity on a Manifold with Boundary

Edward Witten; Petr Horava

REVIEW

Eleven-Dimensional Supergravity on a Manifold with Boundary

Petr Horava, Edward Witten

High Energy Physics - Theory · Submitted 21 Mar 1996 · 8 references

Pith's verdict: The λ² relation is the real result and it holds up; the rest of the paper is honest scaffolding around it, including the parts the authors say don't work.

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arXiv IDhep-th/9603142 (version 1)

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CitationEdward Witten, Petr Horava. "Eleven-Dimensional Supergravity on a Manifold with Boundary." arXiv:hep-th/9603142 (1996). https://pith.science/paper/HJIKBEQR

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Editor's note

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The thing to take away: this paper fixes a number that ten-dimensional string theory leaves free. λ² = 2π(4πκ²)^{2/3}, equivalently η = 128π⁵. The mechanism is clean and worth knowing. The modified Bianchi identity forces C to shift under gauge transformations, which turns the bulk C∧G∧G term — previously an unexplained topological-looking piece of Cremmer-Julia-Scherk — into a Green-Schwarz term. Its gauge variation matches the E₈ five-gluino anomaly. That is the load-bearing chain, and it is short enough to check by hand in an afternoon. What is genuinely new here: the λ² relation, the reinterpretation of C∧G∧G, the boundary-localized anomaly picture, and the observation that the independently known X₈ = -1/8 trR⁴ + 1/32 (trR²)² reproduces the quartic part of the heterotic Î₈. That last one is the strongest evidence in the paper, because X₈ came from two unrelated places — the Type IIA one-loop computation and five-brane anomaly cancellation — and the authors did not fit it. Soft spots, in proportion. The stress-test's worry about the coefficient is fair in principle but small in practice: the chain (2.9)→(2.10)→(2.15)→(2.19)→(3.3)→(3.4)→(3.7) is displayed, and the step from (3.4) to (3.7) is coefficient matching against the E₈ identity, not hidden algebra. What is compressed is the gamma-matrix work behind (2.10) and (2.15), which is standard supergravity practice, and the authors flag the orbifold factor of 2 in footnote 3 rather than burying it. The real soft spot is the one they name themselves: trR² in (3.8)/(3.9) is inserted because anomalies require it, not derived, and Î₄ has no a priori prediction. That bounds the gravitational and mixed results and the Î₈ tests, not λ². Section 4 is a different matter — the δ(0) terms are a symptom, the authors say so plainly, and the four-fermi construction is scaffolding rather than result. Who should read it: anyone working on heterotic M-theory, anomaly inflow, or the M-theory/string dictionary. Read the anomaly section closely; skim Section 4 for the candid admission of where the classical treatment dies. Peer review: yes, send it out. Real result, checkable derivation, limits stated.

Referee report

Significance

If correct, this is a foundational result. The relation λ² = 2π(4πκ²)^{2/3} is a parameter-free prediction: the eleven-dimensional theory has no dilaton or other scalar to adjust the ratio of gauge to gravitational coupling, so the anomaly argument fixes a number that would otherwise be arbitrary. The paper also supplies a rationale for two terms whose role had been obscure — the C∧G∧G interaction and the C∧X₈ coupling — and predicts the relative coefficient of trR⁴ and (trR²)² in Î₈, a structure with no perturbative-string rationale. The internal consistency of the paper's own numbers is a genuine strength: substituting (3.7) into (2.10) reproduces the coefficient of (1.13), and substituting (1.4) into (1.3) gives η = 128π⁵, so the five equations that carry the headline result agree with one another. The paper is also candid about where the classical construction fails, stating in Section 4 that the theory 'only really makes sense at the quantum level.'

Major objections (1)

[Section 3, Eqs. (3.3)–(3.7)] The step from (3.4) and (3.6) to (3.7) is the load-bearing computation of the paper, and it is presented as a single assertion: the reader is asked to accept that the coefficient κ⁴/(128λ⁶) in (3.4) matches 15/(8(4π)⁵5!) in (3.6) to yield λ² = 2π(4πκ²)^{2/3}. Because the result is a definite number, and because the chain passes through the antisymmetrizer normalization of trF_[ABF_CD] fixed in footnote 1, the 1/(6√2) in (2.15), the step-function boundary value (2.19), and the orbifold factor of 2 discussed in footnote 3, a displayed two-line computation (or a short appendix) would let the reader verify the normalization rather than reconstruct it. I note that the paper's own numbers are mutually consistent — substituting (3.7) into (2.10) reproduces the coefficient of (1.13), and (1.4) into (1.3) gives η = 128π⁵ — which is a useful check on internal consistency but does not by itself fix the absolute match against the anomaly normalization conventions of (3.5). This does not block acceptance; it is a request for transparency on the one number the paper asks the reader to take on trust.

Minor objections (8)

[Eq. (4.14) versus Eq. (4.1)] The overall sign of the boundary Lagrangian differs between the two equations: (4.1) carries an overall minus in front of the ¼trF_AB F^AB term, while (4.14) carries a plus in front of the same term. Since (4.14) is presented as a summary of L₀ + L₁ + L₂ + L₃ + L₄, this appears to be a typographical sign and should be corrected or the convention change stated.
[Abstract versus Section 3.1] The abstract (sentence s2) advertises 'several striking new tests,' whereas Section 3.1 states plainly that 'There are therefore three predictions, of which we have here verified two,' the third requiring 'a more precise comparison of different conventions.' Calibrating the abstract to the body's own count would be more accurate.
[Section 3.1, Eqs. (3.8)–(3.9)] The trR² term in the modified Bianchi identity and in the boundary value of G is inserted by inference rather than derived, and the authors say so explicitly ('not required by the low energy supergravity'). Since the gravitational and mixed anomaly results, and the Î₈ prediction that follows, are conditional on this inference, a sentence in the introduction flagging that status would prevent a reader from mistaking those results for an independent eleven-dimensional derivation.
[Abstract, sentence s2] The claim that the argument 'uniquely determines the gauge group to be a copy of E₈' rests on the E₈ identity TrW⁶ = (TrW²)³/7200, described in Section 3 as 'wonderful and unique (to E₈).' One sentence stating why other groups fail — namely that for them TrW⁶ is not a perfect cube of TrW², so the anomaly polynomial does not factorize as (3.4) requires — would make the uniqueness claim self-contained.
[Footnote 1] The definition 'G_IJKL = ∂_I C_JKL ± 2/3 terms' is ambiguous as written; presumably this means the standard weight-one antisymmetrization with the 2/3 coefficient in the Chern-Simons contribution. Please state the convention explicitly, since the normalization propagates into (2.10) and (3.4).
[Reference [5]] Reference [5] (Harvey and Blum) is listed as unpublished. The five-brane argument for X₈ is independently supported by the published references [4] and [6], so the substance is unaffected, but the citation should be updated or the reliance on it reduced.
[Section 4.2, Eq. (4.8)] The argument that no χψ₁₁η corrections to δχ exist is carried by the notation '...' standing for 'all possible combinations of Γ matrices.' Spelling out the two or three structures that actually appear would make the argument checkable rather than schematic.
[Eq. (3.5)] The factor of 1/2 in front of the anomaly coefficient is presumably the Majorana-Weyl halving; a brief parenthetical would help the reader follow the normalization into (3.6).

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The paper

The paper claims

Eleven-dimensional supergravity on a space with a boundary is consistent only if the boundary carries an $E_8$ gauge theory whose coupling is fixed by gravity, and the anomaly algebra says which value.

The reading

The paper asks whether eleven-dimensional supergravity can be placed on a space that ends at a boundary, with a ten-dimensional gauge multiplet living only on that boundary, and whether the combined system can be made consistent. The authors argue that it can, but only for one gauge group and one value of the gauge coupling: a copy of $E_8$ on each boundary component, with $G$ and the gauge coupling tied by $2$, $4$ and $6$ powers of the respective coupling constants, giving $G^2 = 2(4)^2$ in units where the gravitational coupling is $1$. The route is anomaly cancellation: the classical Lagrangian with boundary gauge fields fails to be gauge invariant, the failure has exactly the shape of the ten-dimensional $E_8$ five-gluino anomaly, and the two cancel only for a single numerical value. The reason this matters is that the strong-coupling limit of the $E_8$ heterotic string has no adjustable parameter to absorb such a number, so a definite prediction is a genuine test of the eleven-dimensional picture rather than a fit. The authors also show that the theory cannot be fully consistent classically: the gauge kinetic term is a higher-order correction, and the construction produces formally infinite terms that they expect a proper quantum treatment to cut off.

What carries the argument

The load-bearing device is the modified Bianchi identity $dG = c$ times a boundary delta function times the four-form $F^2 - R^2/2$, together with the resulting gauge transformation law for the three-form. Combined with the bulk interaction of eleven-dimensional supergravity, this converts a term that looked topological into the Green-Schwarz mechanism, and the factorization of the twelve-form into a product of a four-form and an eight-form is what makes the cancellation possible at all. The second device is the eight-form built from the Riemann tensor, fixed independently by five-brane anomaly cancellation and by a one-loop Type IIA computation, which supplies an a priori prediction for the eight-form factor that the eleven-dimensional argument then has to match.

Extended reading notes

Core claim

The central claim is that eleven-dimensional supergravity on a manifold with boundary, or equivalently on an orbifold with codimension-one fixed points, reproduces the anomaly structure of the ten-dimensional $E_8$ heterotic string and fixes its free parameters. The mechanism is a correction to the Bianchi identity for the three-form field strength, supported at the boundary as a delta function and proportional to the gauge and gravitational curvature four-form. That correction forces the three-form to transform under gauge transformations, which turns the familiar bulk interaction into a Green-Schwarz term whose gauge variation matches the anomalous variation of the boundary gluinos. Matching the two determines the gauge coupling in terms of the gravitational coupling, and the gauge group is forced to be $E_8$ because only for $E_8$ does the sixth-order trace factorize into a product of second-order traces. Extending the same logic to gravitational and mixed anomalies requires a second bulk interaction, the three-form wedged with an eight-form built from the Riemann tensor, and the authors observe that the combination of curvature terms needed there is exactly the one that appears in the anomaly eight-form of the heterotic string, a structure that had no explanation in perturbative string theory.

Load-bearing premise

The curvature-squared terms in the modified Bianchi identity and in the boundary value of the three-form field strength are inserted because anomaly cancellation requires them, not derived from eleven-dimensional supergravity, and the authors say so explicitly, so the gravitational and mixed-anomaly conclusions rest on that inference rather than on a computation.

Editorial extensions

If this is right

The gauge group on each boundary component is forced to be $E_8$, since the factorization of the sixth-order trace that anomaly cancellation requires holds only for that group.
The gauge coupling and the gravitational coupling are related by a fixed numerical coefficient, so the eleven-dimensional description of the strongly coupled heterotic string has no free dimensionless parameter left.
The eight-form appearing in the anomaly polynomial is predicted to be a multiple of the square of the four-form plus a curvature-only eight-form, and the relative coefficient of the two curvature quartic terms agrees with the value obtained from five-brane and Type IIA considerations.
Because the gauge kinetic term is a higher-order correction relative to the gravitational action, the theory with boundary gauge fields is not gauge invariant classically and only makes sense once quantum anomalies are included.

Reading between the lines

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

If the coupling relation is right, it gives a sharp handle on the eleven-dimensional origin of the heterotic string: any independent determination of the boundary gauge coupling, for instance from a brane or compactification computation, becomes a check rather than an input.
The same anomaly-matching logic should apply to orbifolds with more than two fixed points, which suggests a family of boundary gauge sectors whose couplings are all tied to the same gravitational constant and whose groups are constrained by the same trace factorization.
The paper's own admission that the curvature-squared term in the Bianchi identity is inserted rather than derived suggests that a genuinely eleven-dimensional derivation of that term, presumably from the full quantum theory, is the natural next target, and would convert the eight-form prediction from a consistency check into a computation.

Original abstract

In this paper, we present a systematic analysis of eleven-dimensional supergravity on a manifold with boundary, which is believed to be relevant to the strong coupling limit of the $E_8\times E_8$ heterotic string. Gauge and gravitational anomalies enter at a very early stage, and require a refinement of the standard Green-Schwarz mechanism for their cancellation. This uniquely determines the gauge group to be a copy of $E_8$ for each boundary component, fixes the gauge coupling constant in terms of the gravitational constant, and leads to several striking new tests of the hypothesis that there is a consistent quantum $M$-theory with eleven-dimensional supergravity as its low energy limit.

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, 3,083 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.21 · compares with prior results 0.23 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper, we present a systematic analysis of eleven-dimensional supergravity on a manifold with boundary, which is believed to be relevant to the strong coupling limit of the $E_8\times E_8$ heterotic string. Gauge and gravitational anomalies enter at a very early stage, and require a refinement of the standard Green-Schwarz mechanism for their cancellation. This uniquely determines the gauge group to be a copy of $E_8$ for each boundary component, fixes the gauge coupling constant in terms of the gravitational constant, and leads to several striking new tests of the hypothesis that there is a consistent quantum $M$-theory with eleven-dimensional supergravity as its low energy limit.

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	In this paper, we present a systematic analysis of eleven-dimensional supergravity on a manifold with boundary, which is believed to be relevant to the strong coupling limit of the $E_8\times E_8$ heterotic string.	contribution 0.99	0.82	0.07	hedged possibility 0.80
s1	Gauge and gravitational anomalies enter at a very early stage, and require a refinement of the standard Green-Schwarz mechanism for their cancellation.	result 0.65	0.29	0.06	asserted 1.00
s2	This uniquely determines the gauge group to be a copy of $E_8$ for each boundary component, fixes the gauge coupling constant in terms of the gravitational constant, and leads to several striking new tests of the hypothesis that there is a consistent quantum $M$-theory with eleven-dimensional supergravity as its low energy limit.	result 0.87	0.79	0.75	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.94.

What was examined, and what was not

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

References

Works cited (8)

[1]

P. Hoˇ rava and E. Witten, “Heterotic and Type I String Dyn amics from Eleven Di- mensions,” Nucl. Phys. B460 (1996) 506, hep-th/9510209

View on Pith Pith review arXiv 1996
[2]

E. Bergshoeﬀ, M. de Roo, B. de Wit and P. van Nieuwenhuisen , “Ten-Dimensional Maxwell-Einstein Supergravity, its Currents and the Issue of its Auxiliary Fields,” Nucl. Phys. B195 (1982) 97

View on Pith 1982
[3]

G. Chapline and N.S. Manton, “Uniﬁcation of Yang-Mills T heory and Supergravity in Ten Dimensions,” Phys. Lett. B120 (1983) 105

View on Pith 1983
[4]

M.J. Duﬀ, J.T. Liu, and R. Minasian, “Eleven-Dimensiona l Origin of String/String Duality: A One Loop Test,” Nucl. Phys. B452 (1995) 261, hep-th/9506126

View on Pith Pith review arXiv 1995
[5]

J.A. Harvey and J. Blum, unpublished

View on Pith
[6]

E. Witten, “Five-Branes and M -Theory on an Orbifold,” Nucl. Phys. B463 (1996), hep-th/9512219

View on Pith Pith review arXiv 1996
[7]

C. Vafa and E. Witten, “A One-Loop Test of String Duality, ” Nucl. Phys. B447 (1995) 261, hep-th/9505053

View on Pith Pith review arXiv 1995
[8]

E. Cremmer, B. Julia, and J. Scherk, “Supergravity Theor y in 11 Dimensions,” Phys. Lett. B76 (1978) 409. 24

View on Pith 1978

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A four-fermion counterterm on D7-branes makes the ten-dimensional gaugino-condensate action finite and reproduces the four-dimensional supergravity quartic gaugino terms.
Compactifications of ADE conformal matter on a torus
hep-th 2018-06 conditional novelty 6.0 of 10

Six-dimensional ADE conformal matter compactified on a torus with flux produces four-dimensional quiver gauge theories, built uniformly by gluing five-dimensional flux domain walls.
The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
hep-th 2018-04 accept novelty 6.0 of 10

The known R^4 coefficient of the M-theory four-graviton amplitude is rederived from ABJM localization data via the flat-space limit of a Mellin amplitude.
6D RG Flows and Nilpotent Hierarchies
hep-th 2016-01 conditional novelty 6.0 of 10

Nilpotent orbits of a 6D SCFT's flavor symmetry label its possible RG flows, and their partial ordering reproduces the hierarchy of infrared fixed points.
Tao Probing the End of the World
hep-th 2015-04 conditional novelty 6.0 of 10

A spiral 5-brane web (the Tao diagram) yields a combinatorial formula for the E-string partition function that matches known elliptic genera up to four instantons.
6d, N=(1,0) Coulomb Branch Anomaly Matching
hep-th 2014-08 accept novelty 6.0 of 10

A perfect-square anomaly mismatch on the Coulomb branch of a 6d N=(1,0) theory is cancelled by a tensor-multiplet coupling that gives background gauge instantons quantized string charge, verified for the E8[N] theory.
E + E $\rightarrow$ H
hep-th 2014-06 conditional novelty 6.0 of 10

An explicit all-genus formula for the elliptic genus of two E-strings is derived and shown to reproduce the elliptic genus of two E8 x E8 heterotic strings.
Differential cohomology in a cohesive infinity-topos
math-ph 2013-10 conditional novelty 6.0 of 10

Differential cohomology, higher Chern-Weil theory and extended geometric prequantization of higher gauge fields are shown to follow from the axioms of a cohesive infinity-topos.
Refined stable pair invariants for E-, M- and [p,q]-strings
hep-th 2013-08 conditional novelty 6.0 of 10

Refined stable-pair invariants for local del Pezzo and half K3 geometries are computed via mirror symmetry and the refined holomorphic anomaly equation, and are shown to fall into E8 Weyl orbits.
5-dim Superconformal Index with Enhanced En Global Symmetry
hep-th 2012-06 conditional novelty 6.0 of 10

The five-dimensional Sp(1) superconformal index, computed by localization including instantons, organizes into E_{N_f+1} characters for N_f up to 5, confirming the conjectured exceptional global symmetry enhancement.
Twisted differential String and Fivebrane structures
math.AT 2009-10 conditional novelty 6.0 of 10

The Green-Schwarz mechanism and its magnetic dual are shown to be cocycles in twisted differential nonabelian cohomology, whose local L-infinity data reproduces the twisted Bianchi identities.
Generating Ekpyrotic Curvature Perturbations Before the Big Bang
hep-th 2007-02 conditional novelty 6.0 of 10

Entropic perturbations generated during an ekpyrotic contraction can be converted into scale-invariant curvature perturbations at a moduli-space bounce, yielding the observed amplitude and a spectral tilt in the range...
Axions In String Theory
hep-th 2006-05 accept novelty 6.0 of 10

Across heterotic, M-theory, G2-holonomy, and D-brane compactifications, the axion decay constant is generically at or above the GUT scale, except in models where Standard Model gauge fields live on vanishing cycles.
Simple fixed-brane gauges in $S_1/Z_2$ braneworlds
hep-th 2006-04 conditional novelty 6.0 of 10

For Randall-Sundrum two-brane cosmologies with a Schwarzschild-AdS bulk, simple fixed-brane gauges exist and can be built order by order in either time after collision or brane velocity.
Heterotic GUT and Standard Model Vacua from simply connected Calabi-Yau Manifolds
hep-th 2006-03 conditional novelty 6.0 of 10

Explicit three-generation heterotic vacua with flipped SU(5) or Standard Model gauge group are constructed on simply connected Calabi-Yau threefolds, using massless U(1) combinations from line bundles in both E8 factors.
Solitons in the Higgs phase -- the moduli matrix approach --
hep-th 2006-02 conditional novelty 6.0 of 10

The moduli matrix organizes BPS solitons in the Higgs phase and yields their moduli spaces, including Grassmannian wall moduli and half-ADHM vortex moduli.
New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls
hep-th 2001-03 accept novelty 6.0 of 10

A new dual formulation of Type IIA supergravity, coupled to a supersymmetric O8-plane action, gives a BPS D8-O8 domain-wall solution with mass quantized in string units and a maximum wall separation set by the string ...
The domain-wall/QFT correspondence
hep-th 1998-07 accept novelty 6.0 of 10

A single 'dual frame' change of variables turns the near-horizon limit of every Dp-brane into a domain-wall geometry, and the resulting gauged supergravity's gauge group matches the R-symmetry of the brane's worldvolu...
Cosmological moduli problem ameliorated by decaying WIMPs
hep-ph 2026-09 conditional novelty 5.0 of 10

In supersymmetric axion models with R-parity violation, decaying WIMPs remove the moduli-induced dark matter overproduction, leaving a BBN bound that allows moduli as light as about 130 TeV.
The EFT stringy viewpoint on large distances
hep-th 2021-04 conditional novelty 5.0 of 10

A bottom-up proposal identifies infinite-distance limits of 4d EFTs with the RG flows of fundamental axionic strings, and conjectures that the leading tower mass scales as m^2 ~ T^w with w = 1, 2, or 3.
A 10d view on the KKLT AdS vacuum and uplifting
hep-th 2019-02 conditional novelty 5.0 of 10

Including the quartic gaugino term removes the singularities in the ten-dimensional KKLT equations, but the local ten-dimensional procedure still fails to reproduce the KKLT effective field theory.
Understanding KKLT from a 10d perspective
hep-th 2019-02 conditional novelty 5.0 of 10

The integrated trace-reversed 10d Einstein equation is equivalent to extremizing a 10d-derived 4d potential, and with a finite perfect-square gaugino action that potential still admits a KKLT uplift.

See all 74 Pith citations

How the literature uses it

212 arXiv papers cite this in 332 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 · 194 sentences without a confident label

Builds on it 3 papers

This is a global extension of the [ref] [ref] “upstairs" and “downstairs" notions, respectively, to corners.

Corners in M-theory · Formulation using the signature operator · 1.00
As a start, to connect this relationship to the $TT̅+Λ_2$ (or more general $T^2+Λ_d$ [ref] ) approach, one can determine the conditions for a patch boundary in string/M-theory by generalizing the Hořava-Witten analysis of [ref] and determining the implications of the considerations of [ref] .

Snowmass White Paper: Cosmology at the Theory Frontier · Cosmological holography · 0.91
The analysis in this paper has a direct, but non-trivial, extension to strongly coupled heterotic $M$-theory [ref] .

Supersymmetric Hidden Sectors for Heterotic Standard Models · Introduction · 0.85

Uses its method or tool 2 papers

In Sec. [ref], we will compute the anomaly polynomial by combining the analysis of Hořava and Witten [ref] of the anomaly of the $E_8$ end-of-the-world brane and that of Freed, Harvey, Minasian and Moore [ref] of the anomaly of multiple coincident five-branes.

Anomaly polynomial of E-string theories · Introduction · 0.92
We do so using the results of GKP [ref] , including the warping effects required for the leading-order no-scale structure, and the perfect-square-type gaugino condensate term of [ref] (motivated by related structures in M-theory [ref] ).

Understanding KKLT from a 10d perspective · Introduction · 0.91

Uses its data or values 1 paper

Given $m_s∼R_10^1/2M_Pl; 11$, with $R_10$ being the length of the $𝕊^1/ℤ_2$ interval, and using the fact that $e^ϕ≡R_10^3/2$ [ref] , we obtain

Stringy Evidence for a Universal Pattern at Infinite Distance · Heterotic string theory on a CY$_3$ · 0.83

Compares with it 7 papers

These results are in good agreement with the anomaly which has been obtained in Horava-Witten mechanism for 10-dimensional manifold in space plus one dimension in time [ref] .

MOG without anomaly · MOG without anomaly in fourteen dimensions · 1.00
In the form of the second line in [ref] – now equivalently re-expressed in terms of the emergent heterotic gauge flux instead of the $G_4$-flux – this class is seen to be closely related to the 8-class denoted $I_8$ in [ref] : Up to global and relative rescaling of $I_8$ (as on the bottom of [ref] ) both are related by [equation] It might be interesting to understand the potential significance of this relation.

Twistorial Cohomotopy implies Green-Schwarz anomaly cancellation · Introduction and overview · 0.92
We will now compare with 11-dimensional SUGRA on the interval $S^1 / ℤ_2$ [ref] , where the circle coordinate $y^s$ is subject to the orbifold identification $y^s ∼- y^s$.

O-folds: Orientifolds and Orbifolds in Exceptional Field Theory · Decomposition of 11-dimensional SUGRA on interval · 0.93

Cites it as support 1 paper

Our inclusion of a divergent quartic gaugino term in the action was motivated by similar discussions in Hořava-Witten theory [ref] .

Brane gaugino condensate in 10d · Consistency with supersymmetry · 0.99

Cites it as background 111 papers

Such particles are perfectly normal from the perturbative heterotic string theory point of view, but in the strong-coupling dual of the heterotic string — the Hořava–Witten theory [ref] — they pose a paradox.

Deconstructing the E_0 SCFT to Solve the Orbifold Paradox of the Heterotic M Theory · Introduction and Summary · 0.81
In 1995, Horava and Witten have shown that in eleven dimensions, all anomalies in field theory and supergravity can be canceled [ref] .

MOG without anomaly · Introduction · 0.87
It was further suggested that the ten dimensional string theories can be related to eleven dimensional supergravity by compactification on $S_1$ and $S_1/Z_2$ [ref] .

On the Low Energy Spectra of the Nonsupersymmetric Heterotic String Theories · Introduction · 0.91

Discussion

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P. Hoˇ rava and E. Witten, “Heterotic and Type I String Dyn amics from Eleven Di- mensions,” Nucl. Phys. B460 (1996) 506, hep-th/9510209

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E. Bergshoeﬀ, M. de Roo, B. de Wit and P. van Nieuwenhuisen , “Ten-Dimensional Maxwell-Einstein Supergravity, its Currents and the Issue of its Auxiliary Fields,” Nucl. Phys. B195 (1982) 97

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J.A. Harvey and J. Blum, unpublished

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