Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients

Teng, Fei; Yau, Shing–Tung

doi:10.1007/s00220-015-2374-0

Cited by 51 publications

(56 citation statements)

References 17 publications

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“…Although manifolds with non-trivial SU (3) structures form a very large class, 1 a limited set of examples which fit into string theory have been constructed. The explicitly known geometries, suitable for heterotic string compactifications, consist of either homogeneous examples [11][12][13][14] or torus fibrations over certain four-dimensional base spaces [15][16][17]. An interesting solution-generating method is also provided in Ref.…”

Section: Introductionmentioning

confidence: 99%

Calabi-Yau manifolds and SU(3) structure

Larfors

Lukas

Ruehle

2019

J. High Energ. Phys.

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We show that non-trivial SU (3) structures can be constructed on large classes of Calabi-Yau threefolds. Specifically, we focus on Calabi-Yau three-folds constructed as complete intersections in products of projective spaces, although we expect similar methods to apply to other constructions and also to Calabi-Yau four-folds. Among the wide range of possible SU (3) structures we find Strominger-Hull systems, suitable for heterotic or type II string compactifications, on all complete intersection Calabi-Yau manifolds. These SU (3) structures of Strominger-Hull type have a nonvanishing and non-closed three-form flux which needs to be supported by source terms in the associated Bianchi identity. We discuss the possibility of finding such source terms and present first steps towards their explicit construction. Provided suitable sources exist, our methods lead to Calabi-Yau compactifications of string theory with a non Ricci-flat, physical metric which can be written down explicitly and in analytic form.

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Section: Introductionmentioning

confidence: 99%

Calabi-Yau manifolds and SU(3) structure

Larfors

Lukas

Ruehle

2019

J. High Energ. Phys.

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“…An interesting feature of the Hull-Strominger equations will emerge, which is that solutions may require a different connection on the Gauduchon line of metrics associated to a Hermitian metric than the Chern unitary connection. This had been anticipated in the physics literature [5,9,37,56], and worked out explicitly by Fei and Yau [36] for stationary points. The only caveat is that we shall be dealing with non-compact settings, which may not behave exactly in the same way as in the compact case.…”

Section: The Case Of Unimodular Lie Groupsmentioning

confidence: 75%

New curvature flows in complex geometry

Phong

Picard

Zhang

2017

Surveys in Differential Geometry

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The Anomaly flow is a flow of (2, 2)-forms on a 3-fold which was originally motivated by string theory and the need to preserve the conformally balanced property of a Hermitian metric in the absence of a ∂∂-Lemma. It has revealed itself since to be a remarkable higher order extension of the Ricci flow. It has also led to several other curvature flows which may be interesting from the point of view of both non-Kähler geometry and the theory of non-linear partial differential equations. This is a survey of what is known at the present time about these new curvature flows.

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“…They include invariant solutions on Lie groups and their quotients (see e.g. Grantcharov [20], Fernandez, Ivanov, Ugarte and Villacampa [14], Otal, Ugarte and Villacampa [27], Fei and Yau [12], and references therein) using connections which are not always Chern connections. They also include local models, such as torus bundles over an ALE space (Fu, Tseng, and Yau [16]), torus bundles over conformally T 4 manifolds (Fernandez, Ivanov, Ugarte, and Vassilev [13]) and a local model based on the twistor space of a hyperkähler manifold (Fei [10]).…”

Section: Some Special Solutions Of the Hull-strominger Systemmentioning

confidence: 99%

Supersymmetric String Vacua with Torsion and Geometric Flows

Phong¹,

Picard²,

Zhang³

2017

Proceedings of Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2016)

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In memoriam of Ioannis BakasIn 1986, a system of equations for compactifications of the heterotic string which preserve supersymmetry was proposed independently by C. Hull and A. Strominger. They are more complicated than the Calabi-Yau compactifications proposed earlier by P. Candelas, G. Horowitz, A. Strominger, and E. Witten, because they allow non-vanishing torsion and they incorporate terms which are quadratic in the curvature tensor. As such they are also particularly interesting from the point of view of both non-Kaehler geometry and the theory of non-linear partial differential equations. While the complete solution of such partial differential equations seems out of reach at the present time, we describe progress in developing a new general approach based on geometric flows which shares some features with the Ricci flow. In particular, this approach can recover the non-perturbative solutions found in 2006 by

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Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients

Cited by 51 publications

References 17 publications

Calabi-Yau manifolds and SU(3) structure

Calabi-Yau manifolds and SU(3) structure

New curvature flows in complex geometry

Supersymmetric String Vacua with Torsion and Geometric Flows

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