Generalized Compactification in Heterotic String Theory

Cyril Matti

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Generalized Compactification in Heterotic String Theory

Cyril Matti

High Energy Physics - Theory · Submitted 15 Apr 2012

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

The authors' main claim They are found to be a generalization of half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.52 · compares with prior results 0.77 · mentions code or data availability 0.02.

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In this thesis, we consider heterotic string vacua based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold preserving only two supercharges. Thus, they correspond to half-BPS states of heterotic supergravity. The constraints on the internal manifolds with SU(3) structure are derived. They are found to be a generalization of half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that heterotic compactifications on half-flat mirror manifolds are based on this class of solutions. Furthermore, within this context, we construct specific examples based on six-dimensional nearly-Kahler homogeneous manifolds and non-trivial vector bundles thereon. Our solutions are based on three specific group coset spaces satisfying the half-flat torsion class conditions. It is shown how to construct line bundles over these manifolds, compute their properties and build up vector bundles consistent with supersymmetry and the heterotic anomaly cancellation. It turns out that the most interesting solutions are obtained from $SU(3)/U(1)^2$. This space supports a large number of vector bundles leading to consistent heterotic vacua with GUT group and, for some of them, with three chiral families.

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 thesis, we consider heterotic string vacua based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold preserving only two supercharges.	contribution 0.95	0.75	0.07	asserted 0.96
s1	Thus, they correspond to half-BPS states of heterotic supergravity.	interpretation 0.88	0.23	0.06	asserted 1.00
s2	The constraints on the internal manifolds with SU(3) structure are derived.	contribution 0.68	0.87	0.11	asserted 0.99
s3	They are found to be a generalization of half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases.	result 0.94	0.91	0.46	asserted 1.00
s4	We also verify that heterotic compactifications on half-flat mirror manifolds are based on this class of solutions.	result 0.76	0.86	0.08	asserted 1.00
s5	Furthermore, within this context, we construct specific examples based on six-dimensional nearly-Kahler homogeneous manifolds and non-trivial vector bundles thereon.	contribution 0.95	0.94	0.08	asserted 1.00
s6	Our solutions are based on three specific group coset spaces satisfying the half-flat torsion class conditions.	contribution 0.53	0.83	0.10	asserted 1.00
s7	It is shown how to construct line bundles over these manifolds, compute their properties and build up vector bundles consistent with supersymmetry and the heterotic anomaly cancellation.	method 0.82	0.89	0.06	asserted 1.00
s8	It turns out that the most interesting solutions are obtained from $SU(3)/U(1)^2$.	result 0.97	0.87	0.21	asserted 0.99
s9	This space supports a large number of vector bundles leading to consistent heterotic vacua with GUT group and, for some of them, with three chiral families.	result 0.97	0.88	0.34	asserted 0.98

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

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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

The paper

Original abstract

In this thesis, we consider heterotic string vacua based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold preserving only two supercharges. Thus, they correspond to half-BPS states of heterotic supergravity. The constraints on the internal manifolds with SU(3) structure are derived. They are found to be a generalization of half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that heterotic compactifications on half-flat mirror manifolds are based on this class of solutions. Furthermore, within this context, we construct specific examples based on six-dimensional nearly-Kahler homogeneous manifolds and non-trivial vector bundles thereon. Our solutions are based on three specific group coset spaces satisfying the half-flat torsion class conditions. It is shown how to construct line bundles over these manifolds, compute their properties and build up vector bundles consistent with supersymmetry and the heterotic anomaly cancellation. It turns out that the most interesting solutions are obtained from $SU(3)/U(1)^2$. This space supports a large number of vector bundles leading to consistent heterotic vacua with GUT group and, for some of them, with three chiral families.

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3 arXiv papers cite this in 7 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 · 6 sentences without a confident label

Cites it as support 1 paper

As we shall see, the zeroth order solution is not sufficient to stabilise the geometric moduli of the internal space $X_6$, as has been pointed out before [ref] .

Moduli in General $SU(3)$-Structure Heterotic Compactifications · Four-Dimensional Domain Walls · 0.96

What it cites · 59 sentences without a confident label

Uses the method or tool of 6 papers

This question will be answered using the $G$-structure formalism [ref] applied to the heterotic case for the groups $G_2$ and $SU(3)$.

The intrinsic torsion of SU(3) and G_2 structures · Motivations and outline · 0.97
This question will be answered using the $G$-structure formalism [ref] applied to the heterotic case for the groups $G_2$ and $SU(3)$.

Non-Kaehler String Backgrounds and their Five Torsion Classes · Motivations and outline · 0.97
This question will be answered using the $G$-structure formalism [ref] applied to the heterotic case for the groups $G_2$ and $SU(3)$.

Stable forms and special metrics · Motivations and outline · 0.97

Compares with 3 papers

We would like to show that the four-dimensional domain wall [ref] indeed matches our $10$-dimensional solution [ref] in a way similar to what happens in the context of type IIA [ref] .

Domain wall flow equations and SU(3)xSU(3) structure compactifications · Comparison between ten and four dimensions · 0.95
We would like to show that the four-dimensional domain wall [ref] indeed matches our $10$-dimensional solution [ref] in a way similar to what happens in the context of type IIA [ref] .

Domain Walls, Hitchin's Flow Equations and G_2-Manifolds · Comparison between ten and four dimensions · 0.95
This is analogous to the original type II mirror symmetry correspondence with NS-NS flux [ref] .

Mirror Symmetry in Generalized Calabi-Yau Compactifications · $G_2/SU(3)$ · 0.90

Cites as background 15 papers

Heterotic compactifications on half-flat mirror manifolds have been studied in Refs. [ref] and, here, we briefly review the main results.

Heterotic String Compactifications on Half-flat Manifolds II · Mirror half-flat manifolds · 0.93
Heterotic compactifications on half-flat mirror manifolds have been studied in Refs. [ref] and, here, we briefly review the main results.

Heterotic on Half-flat · Mirror half-flat manifolds · 0.93
This would be the basis for finding in subsequent work a complete solution perturbatively at all orders, see Refs. [ref] for a general discussion of the $α'$ expansion.

Anomaly, Fluxes and (2,0) Heterotic-String Compactifications · Killing spinor equations and Bianchi identity · 0.95

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