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51
The Srní lectures on nonintegrable geometries with torsion
 Arch. Math. (Brno
, 2006
"... Abstract. This review article intends to introduce the reader to nonintegrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections ..."
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Cited by 58 (8 self)
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Abstract. This review article intends to introduce the reader to nonintegrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skewsymmetric torsion are exhibited as one of the main tools to understand nonintegrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of intrinsic torsion and characteristic connection of a Gstructure as unifying principles. The General Holonomy Principle bridges over to parallel objects, thus motivating the discussion of geometric stabilizers, with emphasis on spinors and differential forms. Several Weitzenböck formulas for Dirac operators associated with torsion connections enable us to discuss spinorial field equations, such as those governing the common sector of type II superstring theory.
HETEROTIC SUPERSYMMETRY, ANOMALY CANCELLATION AND EQUATIONS OF MOTION
, 2009
"... We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion up to two loops in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an instanton. For heterotic compactifications in dimen ..."
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Cited by 25 (1 self)
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We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion up to two loops in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an instanton. For heterotic compactifications in dimension six this fixes an unique choice of the connection on the tangent bundle in the α′ correction of the anomaly cancellation.
A ThreeGeneration CalabiYau Manifold with
 Small Hodge Numbers,” Fortsch. Phys
"... We present a complete intersection CalabiYau manifold Y that has Euler number −72 and which admits free actions by two groups of automorphisms of order 12. These are the cyclic group Z12 and the nonAbelian dicyclic group Dic3. The quotient manifolds have χ = −6 and Hodge numbers (h11, h21) = (1, ..."
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Cited by 23 (5 self)
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We present a complete intersection CalabiYau manifold Y that has Euler number −72 and which admits free actions by two groups of automorphisms of order 12. These are the cyclic group Z12 and the nonAbelian dicyclic group Dic3. The quotient manifolds have χ = −6 and Hodge numbers (h11, h21) = (1, 4). With the standard embedding of the spin connection in the gauge group, Y gives rise to an E6 gauge theory with 3 chiral generations of particles. The gauge group may be broken further by means of the Hosotani mechanism combined with continuous deformation of the background gauge field. For the nonAbelian quotient we obtain a model with 3 generations with the gauge group broken to that of the standard model. Moreover there is a limit in which the quotients develop 3 conifold points. These singularities may be resolved simultaneously to give another manifold with (h11, h21) = (2, 2) that lies right at the tip of the distribution of Calabi–Yau manifolds. This strongly suggests that there is a heterotic vacuum for this manifold that derives from the 3 generation model on the quotient of Y. The manifold Y may also be realised as a hypersurface in the toric variety. The symmetry group does not act torically, nevertheless we are able to identify the mirror of the quotient manifold by adapting the construction of Batyrev. ar X iv
Heterotic flux compactifications and their moduli
, 2006
"... We study supersymmetric compactification to four dimensions with nonzero Hflux in heterotic string theory. The background metric is generically conformally balanced and can be conformally Kähler if the primitive part of the Hflux vanishes. Analyzing the linearized variational equations, we write ..."
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Cited by 21 (3 self)
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We study supersymmetric compactification to four dimensions with nonzero Hflux in heterotic string theory. The background metric is generically conformally balanced and can be conformally Kähler if the primitive part of the Hflux vanishes. Analyzing the linearized variational equations, we write down necessary conditions for the existence of moduli associated with the metric. In a heterotic model that is dual to a IIB compactification on an orientifold, we find the metric moduli in a fixed Hflux background via duality and check that they satisfy the required conditions. We also discuss expressing the conditions for moduli in a fixed flux background using twisted differential operators.
Heterotic nonKähler geometries via polystable bundles on CalabiYau threefolds
 J. Geom. Phys
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Supersymmetric heterotic string backgrounds
, 2007
"... We present the main features of the solution of the gravitino and dilatino Killing spinor equations derived in hepth/0510176 and hepth/0703143 which have led to the classification of geometric types of all type I backgrounds. We then apply these results to the supersymmetric backgrounds of the het ..."
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Cited by 12 (2 self)
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We present the main features of the solution of the gravitino and dilatino Killing spinor equations derived in hepth/0510176 and hepth/0703143 which have led to the classification of geometric types of all type I backgrounds. We then apply these results to the supersymmetric backgrounds of the heterotic string. In particular, we solve the gaugino Killing spinor equation together with the other two Killing spinor equations of the theory. We also use our results to classify all supersymmetry conditions of tendimensional gauge theory.
Geometric transitions, flops and nonKähler manifolds: I
, 2004
"... We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in Mtheory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known p ..."
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Cited by 11 (6 self)
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We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in Mtheory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known phenomena studied earlier in the literature and allows us to describe some new and interesting aspects in a simple and elegant fashion. A precise supergravity description of new torsional manifolds that appear on the type IIA side with branes and fluxes and the corresponding geometric transition are obtained. A local description of new G2 manifolds that are circle fibrations over nonKähler manifolds
Heterotic compactifications on nearly Kähler manifolds
 JHEP 1009 (2010) 074, arXiv:1007.0236 [hepth
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