Flux compactification on smooth, compact three-dimensional toric varieties

Larfors, Magdalena; Lüst, Dieter; Tsimpis, Dimitrios

doi:10.1007/jhep07(2010)073

Cited by 19 publications

(72 citation statements)

References 44 publications

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“…[18]. For type II compactifications, example geometries have been constructed on twistor spaces [19][20][21], on more generic cosets [22], solvmanifolds [23] and on toric varieties [24][25][26]. While these geometries have led to interesting examples of string vacua, their construction is somewhat tedious.…”

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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“…Thus the problem of constructing SU (3) structures on SCTV is reduced to the problem of constructing one-forms K satisfying the requirements of [1]. Although that reference gave some examples of suitable one-forms, and many more were subsequently constructed in [2], no general formula for K exists satisfying the requirements of [1]. As a result, the search for SU (3) structures on SCTV had up to now proceeded on a case-by-case basis.…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper we extend the formalism of [1] for SCTV to construct globally-defined SU (3) structures on the class CP 1 over M , where M is an arbitrary two-dimensional SCTV. As in [1], our construction is based on the existence of a one-form K which, in our case, is naturally distinguished by the structure of the bundle. This one-form does not have the right U (1) charge (in symplectic-quotient terminology) for the procedure of [1] to go through.…”

Section: Introductionmentioning

confidence: 99%

“…As in [1], our construction is based on the existence of a one-form K which, in our case, is naturally distinguished by the structure of the bundle. This one-form does not have the right U (1) charge (in symplectic-quotient terminology) for the procedure of [1] to go through. A different procedure is used instead, exploiting the local SU (2) structure of the base M of the fibration.…”

Section: Introductionmentioning

confidence: 99%

“…The outline of the remainder of paper is as follows. In section 2 we review the formalism of [1] for SCTV, and introduce the tools that will be used in the rest of the paper. The toric CP 1 bundles are described in section 2.4.…”

Section: Introductionmentioning

confidence: 99%

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SU(3) structures on S2 bundles over four-manifolds

Terrisse

Tsimpis

2017

J. High Energ. Phys.

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We construct globally-defined $SU(3)$ structures on smooth compact toric varieties (SCTV) in the class of $\mathbb{CP}^1$ bundles over $M$, where $M$ is an arbitrary SCTV of complex dimension two. The construction can be extended to the case where the base is K\"ahler-Einstein of positive curvature, but not necessarily toric, and admits a parameter space which includes $SU(3)$ structures of LT type.Comment: 35 page

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Lectures on generalized complex geometry for physicists

Koerber

2010

Fortschritte der Physik

100

139

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In these lectures we review Generalized Complex Geometry and discuss two main applications to string theory: the description of supersymmetric flux compactifications and the supersymmetric embedding of D-branes. We start by reviewing G-structures, and in particular SU(3)-structure and its torsion classes, before extending to Generalized Complex Geometry. We then discuss the supersymmetry conditions of type II supergravity in terms of differential conditions on pure spinors, and finally introduce generalized calibrations to describe D-branes. As examples we discuss in some detail AdS4 compactifications, which play a role as the geometric duals in the AdS4/CFT3-correspondence.www.fp-journal.org P. Koerber: Lectures on generalized complex geometry for physicists 1.2 Invitation: supersymmetry conditions in the fluxless case As a warm-up we will study the conditions for unbroken supersymmetry in compactifications without fluxes and see how the condition for a Calabi-Yau geometry comes about. This is also excellently reviewed in a lot more detail in [28, Chap. 15].The bosonic sector of type II supergravity (see appendix B for a brief review) contains, next to the metric and the dilaton, a bunch of form fields, which come from both the NSNS-and the RR-sector of string theory. Putting the vacuum expectation values of these fields -the so-called fluxes -to zero, it turns out that a state with some unbroken supersymmetry solves the equations of motion. This is well-known for theories with global supersymmetry, where the Hamiltonian can be written as a sum of squares and possibly a topological term. The squares vanish precisely when there is unbroken supersymmetry so that the supersymmetric configuration is a global minimum within its topological class (since the topological term does not vary within this class). The statement is more subtle for local supersymmetry, but it still holds for supergravity in the fluxless case. For the case with fluxes we will provide the exact statement in Sect. 4 (Theorem 4.1). The bottom line is that one can construct solutions to the full supergravity equations of motion by solving the relatively simpler supersymmetry conditions. Let us proceed with such fluxless compactifications to 4D Minkowski space. This means we split the total 10D space-time in a 4D uncompactified part with flat Minkowski metric and an internal part with -to be determined -curved metric. Then we follow the strategy of constructing solutions by imposing unbroken supersymmetry. This means that there must be some fraction of the supersymmetry generators for which the supersymmetry variations of all the fields vanish.It turns out that the variations of the bosonic fields always contain a fermionic field. Therefore, if we put the vacuum expectation values of all the fermionic fields to zero in our background, the variations of the bosonic fields automatically vanish. In fact, we must put the vacuum expectation values of all fermionic fields to zero, since they would not be compatible with the compactification ansatz, which ...

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Flux compactification on smooth, compact three-dimensional toric varieties

Cited by 19 publications

References 44 publications

Calabi-Yau manifolds and SU(3) structure

Calabi-Yau manifolds and SU(3) structure

SU(3) structures on S2 bundles over four-manifolds

Lectures on generalized complex geometry for physicists

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