A no-go theorem for string warped compactifications

G. Papadopoulos; S. Ivanov

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A no-go theorem for string warped compactifications

S. Ivanov, G. Papadopoulos

High Energy Physics - Theory · Submitted 30 Aug 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are those on Calabi-Yau manifolds with constant dilaton.

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We give necessary conditions for the existence of perturbative heterotic and common sector type II string warped compactifications preserving four and eight supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are those on Calabi-Yau manifolds with constant dilaton. We obtain similar results for compactifications to six and to two dimensions.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We give necessary conditions for the existence of perturbative heterotic and common sector type II string warped compactifications preserving four and eight supersymmetries to four spacetime dimensions, respectively.	contribution 0.94	0.94	0.35	asserted 0.99
s1	In particular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are those on Calabi-Yau manifolds with constant dilaton.	result 1.00	0.94	0.70	asserted 1.00
s2	We obtain similar results for compactifications to six and to two dimensions.	result 0.90	0.93	0.07	asserted 0.99

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Original abstract

We give necessary conditions for the existence of perturbative heterotic and common sector type II string warped compactifications preserving four and eight supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are those on Calabi-Yau manifolds with constant dilaton. We obtain similar results for compactifications to six and to two dimensions.

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References

Forward citations

Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 92 citations worldwide. Full citation record

On the rigidity of special and exceptional geometries with torsion a closed $3$-form
math.DG 2025-11 unverdicted novelty 7.0 of 10

Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.
The Geometry of D=11 Killing Spinors
hep-th 2002-12 accept novelty 7.0 of 10

Supersymmetric backgrounds of eleven-dimensional supergravity split into two geometric classes, SU(5) for timelike Killing vectors and (Spin(7)⋉R^8)×R for null ones, and the timelike class is fixed almost entirely by ...
G-Structures and Wrapped NS5-Branes
hep-th 2002-05 accept novelty 7.0 of 10

Supersymmetric type II backgrounds with NS flux on R^{1,2} x M_7 are exactly equivalent to manifolds with a specific G_2 or SU(3) structure, which yields a new construction method and a compact-manifold vanishing theorem.
Stringy Corrections to Heterotic SU(3)-Geometry
hep-th 2025-07 accept novelty 6.0 of 10

At second order in alpha', heterotic SU(3) compactifications with a smooth large-radius limit obey the same complex geometric equations as Strominger's first-order system, and the Hull connection is not an instanton.
Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications
hep-th 2014-02 conditional novelty 6.0 of 10

The infinitesimal moduli space of the Strominger system equals the first cohomology of a holomorphic structure on an extension bundle built to encode the anomaly cancellation condition.

Show 4 more citing papers

Geometry of type II common sector N=2 backgrounds
hep-th 2006-02 conditional novelty 6.0 of 10

Every type II common-sector N=2 background is either a pp-wave over an eight-manifold with Spin(7), SU(4), or G2 structure, or a null two-torus bundle over the same type of manifold.
Superstrings with Intrinsic Torsion
hep-th 2003-02 accept novelty 6.0 of 10

A case-by-case classification of static supersymmetric NS-NS string backgrounds in terms of G-structures and intrinsic torsion, adding new d=8, d=9 and d=6 geometries to the known list.
Flux compactifications in string theory: a comprehensive review
hep-th 2005-09 accept novelty 3.0 of 10

A structured survey of type II flux compactifications: which fluxes preserve N=1, why compact spaces need orientifold planes, how fluxes generate superpotentials, and how far they go toward fixing moduli.
Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
hep-th 2006-10 unverdicted

A comprehensive pedagogical review of four-dimensional orientifold and flux compactifications with D-branes, assembling model-building rules, effective-action methods, and statistical vacuum counts.

How the literature uses it

20 arXiv papers cite this in 29 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 · 24 sentences without a confident label

Cites it as background 5 papers

Manifolds with $SU(n)$ structures have extensively been explored in the literature, see e.g. [ref] .

Classification, geometry and applications of supersymmetric backgrounds · $SU(4)⋉^8$, $N=2$ · 0.95
It has been known for sometime that compact conformally balanced strong HKT (and CYT) are hyper-Kähler (Calabi-Yau) [ref] .

On the rigidity of special and exceptional geometries with torsion a closed $3$-form · Introduction · 0.91
For a non-exhaustive list of references see [ref] as well as the detailed reviews [ref] .

The Geometry and Superconformal Algebras of String Compactifications with a $G$-structure · Introduction · 0.97

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