Showing papers on "Calabi–Yau manifold published in 2004"
TL;DR: In this paper, the N = 1 low energy effective action for compactifications of type IIB string theory on compact Calabi-Yau orientifolds in the presence of background fluxes from a Kaluza-Klein reduction is determined.
458 citations
TL;DR: In this paper, the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form eiJ and the holomorphic form Ω.
Abstract: We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form eiJ and the holomorphic form Ω. The equations are explicitly symmetric under exchange of the two pure spinors and a choice of even or odd-rank RR field. This is mirror symmetry for manifolds with torsion. Moreover, RR fluxes affect only one of the two equations: eiJ is closed under the action of the twisted exterior derivative in IIA theory, and similarly Ω is closed in IIB. Modulo a different action of the B–field, this means that supersymmetric SU(3)-structure manifolds are all generalized Calabi-Yau manifolds, as defined by Hitchin. An equivalent, and somewhat more conventional, description is given as a set of relations between the components of intrinsic torsions modified by the NS flux and the Clifford products of RR fluxes with pure spinors, allowing for a classification of type II supersymmetric vacua on six-manifolds. We find in particular that supersymmetric six-manifolds are always complex for IIB backgrounds while they are twisted symplectic for IIA.
368 citations
TL;DR: In this paper, the authors compute the N = 1 effective low energy action for a stack of N space-time filling D3-branes in generic IIB Calabi-Yau orientifolds with non-trivial background fluxes by reducing the Dirac-Born-Infeld and Chern-Simons actions.
267 citations
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TL;DR: In this paper, the authors construct a purely algebraic version of Gromov-Witten invariants, which depend on a Calabi-Yau A-infinity category.
Abstract: This is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov-Witten invariants (at all genera). These Gromov-Witten type invariants depend on a Calabi-Yau A-infinity category, which plays the role of the target in ordinary Gromov-Witten theory. When we use an appropriate A-infinity version of the derived category of coherent sheaves on a Calabi-Yau variety, this constructs the B model at all genera. When the Fukaya category of a compact symplectic manifold X is used, it is shown, under certain assumptions, that the usual Gromov-Witten invariants are recovered. The assumptions are that a good theory of open-closed Gromov-Witten invariants exists for X, and that the natural map from the Hochschild homology of the Fukaya category of X to the ordinary homology of X is an isomorphism.
252 citations
TL;DR: For a given complex n-fold M, the authors showed that there is a subclass of 3-folds which has natural families of non-Kahler SU(3)-structures satisfying the conditions for Open image in new window supersymmetry in the heterotic string theory compactified on the 3-fold.
Abstract: For a given complex n-fold M we present an explicit construction of all complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For physical applications we consider the case of M being a Calabi-Yau 2-fold. We show that for such M, there is a subclass of the 3-folds that we construct, which has natural families of non-Kahler SU(3)-structures satisfying the conditions for Open image in new window supersymmetry in the heterotic string theory compactified on the 3-folds. We present examples in the aforementioned subclass with M being a K3-surface and a 4-torus.
249 citations
TL;DR: In this article, the authors present explicit examples of supersymmetric and nonsupersymmetric solutions to the resulting 4d {Nu} = 1 supergravity no-scale supergravity.
Abstract: The presence of RR and NS three-form fluxes in type IIB string compactification on a Calabi-Yau orientifold gives rise to a nontrivial superpotential W for the dilaton and complex structure moduli. This superpotential is computable in terms of the period integrals of the Calabi-Yau manifold. In this paper, we present explicit examples of both supersymmetric and nonsupersymmetric solutions to the resulting 4d {Nu} = 1 supersymmetric no-scale supergravity, including some nonsupersymmetric solutions with relatively small values of W. Our examples arise on orientifolds of the hypersurfaces in WP{sub 1,1,1,1,4}{sup 4} and WP{sub 1,1,2,2,6}{sup 4}. They serve as explicit illustrations of several of the ingredients which have played a role in the recent proposals for constructing de Sitter vacua of string theory.
191 citations
TL;DR: In this paper, the authors provide a self-contained guide to the derived category approach to B-branes and the idea of Pi-stability and argue that this mathematical machinery is hard to avoid for a proper understanding of Bbranes.
Abstract: In this review we study BPS D-branes on Calabi-Yau threefolds. Such D-branes naturally divide into two sets called A-branes and B-branes which are most easily understood from topological field theory. The main aim of this paper is to provide a self-contained guide to the derived category approach to B-branes and the idea of Pi-stability. We argue that this mathematical machinery is hard to avoid for a proper understanding of B-branes. A-branes and B-branes are related in a very complicated and interesting way which ties in with the ``homological mirror symmetry'' conjecture of Kontsevich. We motivate and exploit this form of mirror symmetry. The examples of the quintic 3-fold, flops and orbifolds are discussed at some length. In the latter case we describe the role of McKay quivers in the context of D-branes. These notes are to be submitted to the proceedings of TASI03.
176 citations
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TL;DR: In this paper, the A and B model topological strings on CP^{3|4} were interpreted as equivalent to open N=2 string theory on spacetime with signature (2,2), when covariantized with respect to SO(2, 2) and supersymmetrized a la Siegel.
Abstract: We interpret the A and B model topological strings on CP^{3|4} as equivalent to open N=2 string theory on spacetime with signature (2,2), when covariantized with respect to SO(2,2) and supersymmetrized a la Siegel. We propose that instantons ending on Lagrangian branes wrapping RP^{3|4} deform the self-dual N=4 Yang-Mills sector to ordinary Yang-Mills by generating a `t Hooft like expansion. We conjecture that the A and B versions are S-dual to each other. We also conjecture that mirror symmetry may explain the recent observations of Witten that twistor transformed N=4 Yang-Mills amplitudes lie on holomorphic curves.
125 citations
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TL;DR: In this article, the Calabi-Yau conjecture for embedded surfaces is shown to be true for injective immersions, i.e., surfaces with an injective interior.
Abstract: In this paper we will prove the Calabi-Yau conjectures for embedded surfaces. In fact, we will prove considerably more.
The Calabi-Yau conjectures about surfaces date back to the 1960s. Much work has been done on them over the past four decades. In particular, examples of Jorge-Xavier from 1980 and Nadirashvili from 1996 showed that the immersed versions were false; we will show here that for embedded surfaces, i.e., injective immersions, they are in fact true.
119 citations
TL;DR: A torus fibered Calabi-Yau threefold with first homotopy group 3? 3 is constructed as a free quotient of a fiber product of two dP9 surfaces as mentioned in this paper.
Abstract: A torus fibered Calabi-Yau threefold with first homotopy group 3 ? 3 is constructed as a free quotient of a fiber product of two dP9 surfaces. Calabi-Yau threefolds of this type admit 3 ? 3 Wilson lines. In conjunction with SU(4) holomorphic vector bundles, such vacua lead to anomaly free, three generation models of particle physics with a right handed neutrino and a U(1)B?L gauge factor, in addition to the SU(3)C ? SU(2)L ? U(1)Y standard model gauge group. This factor helps to naturally suppress nucleon decay. The moduli space and Dolbeault cohomology of the threefold is also discussed.
96 citations
TL;DR: In this article, the precise relation between the Kodaira-Spencer path integral and a particular wave function in seven-dimensional quadratic field theory is established, and the special properties of three-forms in 6D, as well as Hitchin's action functional, play an important role.
Abstract: The precise relation between Kodaira-Spencer path integral and a particular wave function in seven dimensional quadratic field theory is established. The special properties of three-forms in 6d, as well as Hitchin's action functional, play an important role. The latter defines a quantum field theory similar to Polyakov's formulation of 2d gravity; the curious analogy with world-sheet action of bosonic string is also pointed out.
TL;DR: In this article, the authors discuss the relationship between the SL(2:R)/U(1) supercoset and N=2 Liouville theory and make a precise correspondence between their representations.
Abstract: We first discuss the relationship between the SL(2:R)/U(1) supercoset and N=2 Liouville theory and make a precise correspondence between their representations. We shall show that the discrete unitary representations of SL(2:R)/U(1) theory correspond exactly to those massless representations of N=2 Liouville theory which are closed under modular transformations and studied in our previous work hep-th/0311141. It is known that toroidal partition functions of SL(2:R)/U(1) theory (2D Black Hole) contain two parts, continuous and discrete representations. The contribution of continuous representations is proportional to the space-time volume and is divergent in the infinite-volume limit while the part of discrete representations is volume-independent. In order to see clearly the contribution of discrete representations we consider elliptic genus which projects out the contributions of continuous representations: making use of the SL(2:R)/U(1), we compute elliptic genera for various non-compact space-times such as the conifold, ALE spaces, Calabi-Yau 3-folds with A_n singularities etc. We find that these elliptic genera in general have a complex modular property and are not Jacobi forms as opposed to the cases of compact Calabi-Yau manifolds.
TL;DR: In this paper, it was shown that it is possible to construct supersymmetric three-generation models with the Standard Model gauge group in the framework of non-simply connected elliptically fibered Calabi-Yau threefolds, without section but with a bi-section.
Abstract: We show that it is possible to construct supersymmetric three-generation models with the Standard Model gauge group in the framework of non-simply-connected elliptically fibered Calabi–Yau threefolds, without section but with a bi-section. The fibrations on a cover Calabi–Yau threefold, where the model has six generations of SU(5) and the bundle is given via the spectral cover description, use a different description of the elliptic fiber which leads to more than one global section. We present two examples of a possible cover Calabi–Yau threefold with a free involution: one is a fiber product of rational elliptic surfaces dP9; another example is an elliptic fibration over a Hirzebruch surface. We compute the necessary amount of chiral matter by "turning on" a further parameter which is related to singularities of the fibration and the branching of the spectral cover.
TL;DR: In this paper, the first in a series of five papers studying special Lagrangian submanifolds (SLV m-folds) X in almost Calabi-Yau m-foldM with singularitiesx1,..., xn locally modelled on special LagrangeianconesC1, Cnin ℂm with isolated singularities at 0.
Abstract: This is the first in a series of five papers studying special Lagrangian submanifolds(SLV m-folds) X in almost Calabi–Yau m-foldsM with singularitiesx1, ..., xn locally modelled on special LagrangianconesC1, ..., Cnin ℂm with isolated singularities at 0. Readers are advised to begin with Paper V.
TL;DR: The relationship between the SL(2;R)/U(1) supercoset and N=2 Liouville theory is discussed in this article, where it is shown that the discrete unitary representations of SL( 2;R/U( 1) theory correspond exactly to those massless representations of N = 2 LiouVILLE theory which are closed under modular transformations.
Abstract: We first discuss the relationship between the SL(2;R)/U(1) supercoset and N=2 Liouville theory and make a precise correspondence between their representations. We shall show that the discrete unitary representations of SL(2;R)/U(1) theory correspond exactly to those massless representations of N=2 Liouville theory which are closed under modular transformations and studied in our previous work hep-th/0311141.
It is known that toroidal partition functions of SL(2;R)/U(1) theory (2D Black Hole) contain two parts, continuous and discrete representations. The contribution of continuous representations is proportional to the space-time volume and is divergent in the infinite-volume limit while the part of discrete representations is volume-independent.
In order to see clearly the contribution of discrete representations we consider elliptic genus which projects out the contributions of continuous representations: making use of the SL(2;R)/U(1), we compute elliptic genera for various non-compact space-times such as the conifold, ALE spaces, Calabi-Yau 3-folds with A_n singularities etc. We find that these elliptic genera in general have a complex modular property and are not Jacobi forms as opposed to the cases of compact Calabi-Yau manifolds.
TL;DR: In this article, the structure group SU(4) gauge vacua of both weakly and strongly coupled heterotic superstring theory compactified on torus-fibered Calabi-Yau threefolds Z with 2 × 2 fundamental group are presented.
Abstract: Structure group SU(4) gauge vacua of both weakly and strongly coupled heterotic superstring theory compactified on torus-fibered Calabi-Yau threefolds Z with 2 × 2 fundamental group are presented. This is accomplished by constructing invariant, stable, holomorphic rank four vector bundles on the simply connected cover of Z. Such bundles can descend either to Hermite-Yang-Mills instantons on Z or to twisted gauge fields satisfying the Hermite-Yang-Mills equation corrected by a non-trivial flat B-field. It is shown that large families of such instantons satisfy the constraints imposed by particle physics phenomenology. The discrete parameter spaces of those families are presented, as well as a lower bound on the dimension of the continuous moduli of any such vacuum. In conjunction with 2 × 2 Wilson lines, these SU(4) gauge vacua can lead to standard-like models at low energy with an additional U(1)B−L symmetry. This U(1)B−L symmetry is very helpful in naturally suppressing nucleon decay.
TL;DR: In this article, the authors show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques.
Abstract: We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this Calabi-Yau.
TL;DR: Grana et al. as mentioned in this paper showed that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form e i J and the holomorphic form Ω.
TL;DR: In this article, the authors compute all loop topological string amplitudes on orientifolds of local Calabi-Yau manifolds, by using geometric transitions involving SO/Sp Chern-Simons the-ory, localization on the moduli space of holomorphic maps with involution, and the topo- logical vertex.
Abstract: We compute all loop topological string amplitudes on orientifolds of local Calabi-Yau manifolds, by using geometric transitions involving SO/Sp Chern-Simons the- ory, localization on the moduli space of holomorphic maps with involution, and the topo- logical vertex. In particular we count Klein bottles and projective planes with any number of handles in some Calabi-Yau orientifolds.
TL;DR: In this paper, the authors studied special Lagrangian submanifolds (SLV m-folds) X in (almost) Calabi-Yau m-foldM with singularities x 1,..., xnlocally modelled on special LRC conesC1,..., Cn in ℂm with isolated singularities at 0.
Abstract: This is the fourth in a series of five papers studying special Lagrangian submanifolds(SLV m-folds) X in (almost) Calabi–Yau m-foldsM with singularities x1,..., xnlocally modelled on special Lagrangian conesC1,..., Cn in ℂm with isolated singularities at 0. Readers are advised to begin with Paper V.
TL;DR: In this article, the authors study five-dimensional Kasner cosmologies in a time-dependent Calabi-Yau compactification of M-theory undergoing a flop transition and analyse the interplay between the geometries of moduli space and spacetime.
Abstract: We study five-dimensional Kasner cosmologies in a time-dependent Calabi–Yau compactification of M-theory undergoing a flop transition. The dynamics of the additional states, which become massless at the transition point and give rise to a scalar potential, are taken into account using a recently constructed gauged supergravity action. Due to the dynamics of these states the moduli do not show the usual run-away behaviour but oscillate around the transition region. Moreover, the solutions typically exhibit short periods of accelerated expansion. We also analyse the interplay between the geometries of moduli space and spacetime.
TL;DR: In this article, the authors derived new crystal melting models from Chern-Simons theory on the three-sphere and showed that these models compute amplitudes for A-model on the resolved conifold.
Abstract: We derive new crystal melting models from Chern-Simons theory on the three-sphere. Via large N duality, these models compute amplitudes for A-model on the resolved conifold. The crystal is bounded by two walls whose distance corresponds to the Kahler modulus of the geometry. An interesting phenomenon is found where the Kahler modulus is shifted by the presence of non-compact D-branes. We also discuss the idea of using the crystal models as means of proving more general large N dualities to all order in $g_s$.
TL;DR: In this article, neutral Calabi-Yau metrics and hypersymplectic structures on some Kodaira manifolds are constructed, and the structures are symmetric with respect to the central tori.
Abstract: We construct neutral Calabi-Yau metrics and hypersymplectic structures on some Kodaira manifolds. Our structures are symmetric with respect to the central tori.
TL;DR: Moret-Bailly's pencil of abelian surfaces and Katsura's analysis of generalized Kummer surfaces were used to construct a smooth Calabi-Yau threefold in characteristic two and three that do not lift to characteristic zero as discussed by the authors.
Abstract: Some smooth Calabi–Yau threefolds in characteristic two and three that do not lift to characteristic zero are constructed. These threefolds are pencils of supersingular K3-surfaces. The construction depends on Moret-Bailly's pencil of abelian surfaces and Katsura's analysis of generalized Kummer surfaces. The threefold in characteristic two turns out to be nonrigid.
TL;DR: In this article, the third in a series of five papers studying special Lagrangian submanifolds (SLVm-folds) X in (almost) Calabi-Yaum foldsM with singularities x1,..., xn locally modelled on special Lagrangeian conesC1, Cn in \(\mathbb{C}\)m with isolated singularities at 0.
Abstract: This is the third in a series of five papers studying special Lagrangian submanifolds(SLVm-folds) X in (almost) Calabi–Yaum-foldsM with singularities x1, ..., xn locally modelled on special Lagrangian conesC1, ..., Cn in \(\mathbb{C}\)m with isolated singularities at 0. Readers are advised to begin with Paper V.
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TL;DR: In this article, the notion of A-model Lagrangian D-branes is defined as introducing defects in the Calabi-Yau crystal and the crystal melting in the presence of these defects reproduces all genus string amplitudes.
Abstract: We define the notion of A-model Lagrangian D-branes as introducing defects in the Calabi-Yau crystal The crystal melting in the presence of these defects reproduces all genus string amplitudes as well as leads to additional non-perturbative terms
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TL;DR: In this paper, the authors use the differential geometrical framework of generalized (almost) Calabi-Yau structures to reconsider the concept of mirror symmetry and show that not only the metric and B-field but also the algebraic structures are uniquely mapped.
Abstract: We use the differential geometrical framework of generalized (almost) Calabi-Yau structures to reconsider the concept of mirror symmetry. It is shown that not only the metric and B-field but also the algebraic structures are uniquely mapped. As an example we use the six-torus as a trivial generalized Calabi-Yau 6-fold and an appropriate B-field.
TL;DR: In this article, the authors compute all loop topological string amplitudes on orientifolds of local Calabi-Yau manifolds, by using geometric transitions involving SO/Sp Chern-Simons theory, localization on the moduli space of holomorphic maps with involution, and the topological vertex.
Abstract: We compute all loop topological string amplitudes on orientifolds of local Calabi-Yau manifolds, by using geometric transitions involving SO/Sp Chern-Simons theory, localization on the moduli space of holomorphic maps with involution, and the topological vertex. In particular we count Klein bottles and projective planes with any number of handles in some Calabi-Yau orientifolds.
TL;DR: In this article, a geometric structure defined by a system of closed exterior differential forms and developed a new approach to deformation problems of geometric structures is considered. But the approach is restricted to geometric structures such as Calabi-Yau, HyperKahler, G2 and Spin(7) structures.
Abstract: This paper focuses on a geometric structure defined by a system of closed exterior differential forms and develops a new approach to deformation problems of geometric structures. We obtain a criterion for unobstructed deformations from a cohomological point of view (Theorem 1.7). Further we show that under a cohomological condition, the moduli space of the geometric structures becomes a smooth manifold of finite dimension (Theorem 1.8). We apply our approach to the geometric structures such as Calabi–Yau, HyperKahler, G2 and Spin(7) structures and then obtain a unified construction of smooth moduli spaces of these four geometric structures. We generalize the Moser's stability theorem to provide a direct proof of the local Torelli type theorem in these four geometric structures (Theorem 1.10).