Showing papers on "Calabi–Yau manifold published in 1995"
TL;DR: Mirror symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed in this article for Calabi-Yau spaces with two and three moduli.
Abstract: Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.
488 citations
TL;DR: In this paper, the authors extend the discussion of mirror symmetry, Picard-Fuchs equations, instanton corrected Yukawa couplings and the topological one-loop partition function to the case of complete intersections with higher dimensional moduli spaces.
382 citations
TL;DR: In this paper, generic features of eleven dimensional supergravity compactified down to five dimensions on an arbitrary Calabi-Yau threefold were considered and the possible relation with the heterotic string compactified on K 3 × S 1 was discussed.
251 citations
TL;DR: Namikawa and Steenbrink as discussed by the authors studied the relationship between local and global deforma- tions of a threefold Z with isolated hypersurface singularities which admits small resolutions.
Abstract: Yoshinori Namikawa I,*, J.H.M. Steenbrink 2 I Department of Mathematics, Sophia University, Kioi-Cho, Tokyo 102, Japan 2 Mathematical Institute, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands Oblatum 10-X-1994 & 13-VI-1995 Introduction Friedman [Fr] has studied the relationship between local and global deforma- tions of a threefold Z with isolated hypersurface singularities which admits small resolutions. One of his main results is as follows. Let Z be a Moishezon threefold with only ordinary double points { Pl ..... p. }. Assume that the canon- ical line bundle
98 citations
TL;DR: In this paper, Batyrev's construction of the missing mirrors in the Calabi-Yau manifold set was used to show that many of these missing mirrors may be interpreted as non-transverse hypersurfaces in weighted P 4's, i.e. hypersurface for which dp vanishes at a point other than the origin.
71 citations
TL;DR: In this article, it has been realized that a large class of Calabi-Yau models in which the VEV of the gauge connection is not set equal to the spin connection is valid classical solutions of string theory.
68 citations
TL;DR: In this paper, a detailed study of the generalized hypergeometric system introduced by Gel'fand, Kapranov and Zelevinski in the context of toric geometry is presented, where the Grobner basis for the toric ideal determines a finite set of differential operators for the local solutions of the GKZ system.
Abstract: We present a detailed study of the generalized hypergeometric system introduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) in the context of toric geometry. GKZ systems arise naturally in the moduli theory of Calabi-Yau toric varieties, and play an important role in applications of the mirror symmetry. We find that the Grobner basis for the so-called toric ideal determines a finite set of differential operators for the local solutions of the GKZ system. At the special point called the large radius limit, we find a close relationship between the principal parts of the operators in the GKZ system and the intersection ring of a toric variety. As applications, we analyze general three dimensional hypersurfaces of Fermat and non-Fermat types with Hodge numbers up to $h^{1,1}=3$. We also find and analyze several non Landau-Ginzburg models which are related to singular models.
57 citations
Book•
01 Jan 1995
TL;DR: An introduction to the subject supergravity and Kahler geometry can be found in this paper, where the authors introduce the subject of Calabi-Yau manifolds, Gepner tensor products moduli spaces and topological field theories.
Abstract: An introduction to the subject supergravity and Kahler geometry Calabi-Yau manifolds N=2 field theories in two dimensions Gepner tensor products moduli spaces and special geometry topological field theories mirror symmetry Picard-Fuchs equations monodromy and duality groups
54 citations
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TL;DR: In this article, the authors studied the smoothability of Calabi-Yau threefold with canonical singularities and obtained strong restrictions on the class of primitive Calabi Yau threefolds.
Abstract: A primitive Calabi-Yau threefold is a non-singular Calabi-Yau threefold which cannot be written as a crepant resolution of a singular fibre of a degeneration of Calabi-Yau threefolds. These should be thought as the most basic Calabi-Yau manifolds; all others should arise through degenerations of these. This paper first continues the study of smoothability of Calabi-Yau threefolds with canonical singularities begun in the author's previous paper, ``Deforming Calabi-Yau Threefolds.'' (alg-geom 9506022). If X' is a non-singular Calabi-Yau threefold, and f:X'->X is a contraction of a divisor to a curve, we obtain results on when X is smoothable. We then discuss applications of this result to the classification of primitive Calabi-Yau threefolds. Combining the deformation theoretic results of this paper with those of ``Deforming Calabi-Yau Threefolds,'' we obtain strong restrictions on the class of primitive Calabi-Yau threefolds. We also speculate on how such work might yield results on connecting together all moduli spaces of Calabi-Yau threefolds.
52 citations
TL;DR: This paper constructed a Calabi-Yau 3-fold whose fundamental group is the quaternion group H = H8 and whose construction is reminiscent of Reid's unpublished construction of a surface with pg = 0, K2 = 2 and π1 = H.
Abstract: This note, written in 1994, answers a question of Dolgachev by constructing a Calabi–Yau threefold whose fundamental group is the quaternion group H = H8 The construction is reminiscent of Reid’s unpublished construction of a surface with pg = 0, K2 = 2 and π1 = H; I explain below the link between the two problems
46 citations
TL;DR: In this article, the authors identify the exactly solvable theory of the conformal fixed point of (0, 2) Calabi-Yau sigma-models and their Landau-Ginzburg phases.
Abstract: We identify the exactly solvable theory of the conformal fixed point of (0,2) Calabi-Yau sigma-models and their Landau-Ginzburg phases. To this end we consider a number of (0,2) models constructed from a particular (2,2) exactly solvable theory via the method of simple currents. In order to establish the relation between exactly solvable (0,2) vacua of the heterotic string, (0,2) Landau-Ginzburg orbifolds, and (0,2) Calabi-Yau manifolds, we compute the Yukawa couplings in the exactly solvable model and compare the results with the product structure of the chiral ring which we extract from the structure of the massless spectrum of the exact theory. We find complete agreement between the two up to a finite number of renormalizations. For a particularly simple example we furthermore derive the generating ideal of the chiral ring from a (0,2) linear sigma-model which has both a Landau-Ginzburg and a (0,2) Calabi-Yau phase.
TL;DR: In this paper, it has been realized that a large class of Calabi-Yau models in which the VEV of the gauge connection is not set equal to the spin connection is valid classical solutions of string theory.
Abstract: It has recently been realized that a large class of Calabi-Yau models in which the VEV of the gauge connection is not set equal to the spin connection of the Calabi-Yau manifold are valid classical solutions of string theory. We provide some examples of three generation models based on such generalized Calabi-Yau compactifications, including models with observable gauge group $SU(3)\times SU(2)\times U(1)$.
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TL;DR: In this article, it was shown that all 7555 Calabi-Yau hypersurfaces in weighted projective four space are mathematically connected by extremal transitions, and the authors extended the known web of interconnections between Calabi Yau manifolds.
Abstract: We review recent work concerning topology changing phase transitions through black hole condensation in Type II string theory. We then also briefly describe a present study aimed at extending the known web of interconnections between Calabi-Yau manifolds. We show, for instance, that all 7555 Calabi-Yau hypersurfaces in weighted projective four space are mathematically connected by extremal transitions.
TL;DR: In this article, a generalisation of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi-Yau threefold.
Abstract: The generalisation of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi--Yau threefold. Duality symmetries of this manifold are connected with the analogous dualities associated with the dynamical Riemann surface of the rigid theory. N=2 rigid gauge theories are reviewed in a framework ready for comparison with the local case. As a byproduct we give in general the full duality group (quantum monodromy) for an arbitrary rigid $SU(r+1)$ gauge theory, extending previous explicit constructions for the $r=1,2$ cases. In the coupling to gravity, R--symmetry and monodromy groups of the dynamical Riemann surface, whose structure we discuss in detail, are embedded into the symplectic duality group $\Gamma_D$ associated with the moduli space of the dynamical Calabi--Yau threefold.
TL;DR: In this article, the authors derived a mass formula for the extreme black holes caused by the self-dual 5-form field strength, which is stable and supersymmetric, which can be written by the moduli parameters of Calabi-Yau manifold and can be calculated explicitly.
Abstract: Recently proposed mechanism of the black hole condensation at conifold singularity in type II string is an interesting idea from which we can interpret the phase of the universal moduli space of the string vacua. It might also be expected that the true physics is on the conifold singularity after supersymmetry breaking. We derive a mass formula for the extreme black holes caused by the self-dual 5-form field strength, which is stable and supersymmetric. It is shown that the formula can be written by the moduli parameters of Calabi-Yau manifold and can be calculated explicitly.
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TL;DR: In this paper, the Bogomolov-Tian-Todorov unobstructedness theorem was generalized to the case of Calabi-Yau threefold with canonical singularities.
Abstract: This paper first generalises the Bogomolov-Tian-Todorov unobstructedness theorem to the case of Calabi-Yau threefolds with canonical singularities. The deformation space of such a Calabi-Yau threefold is no longer smooth, but the general principle is that the obstructions to deforming such a threefold are precisely the obstructions to deforming the singularities of the threefold. Secondly, these results are applied to smoothing singular Calabi-Yau threefolds with crepant resolutions. Any such Calabi-Yau threefold with isolated complete intersection singularities which are not ordinary double points is smoothable. A Calabi-Yau threefold with non-complete intersection isolated singularities is proved to be smoothable under much stronger hypotheses.
TL;DR: In this article, generic features of eleven dimensional supergravity compactified down to five dimensions on an arbitrary Calabi-Yau threefold were considered, and the results showed that these features can be used to obtain a three-dimensional supergravity.
Abstract: We consider generic features of eleven dimensional supergravity compactified down to five dimensions on an arbitrary Calabi-Yau threefold.
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TL;DR: In this paper, the authors focus on determining for which degenerations the central fiber is at finite distance with respect to the Weil-Petersson metric and obtain a simple condition on the limiting mixed Hodge structure.
Abstract: In this paper we focus on determining for which degenerations the central fibre is at finite distance with respect to Weil-Petersson metric. We obtain a simple condition on the limiting mixed Hodge structure. Then we combine the result with the canonical mixed Hodge structure of the central fibre and obtain a simple cohomological condition for the central fibre to be at finite distance. As a corollary, we prove that a central fibre with simple nodes is at finite distance. This issue has been raised in the Physics literature including the recent development of so-called "mass-less black holes".
TL;DR: The moduli space of all Calabi-Yau manifolds that can be realized as hypersurfaces described by a transverse polynomial in a four dimensional weighted projective space is connected.
Abstract: We show that the moduli space of all Calabi-Yau manifolds that can be realized as hypersurfaces described by a transverse polynomial in a four dimensional weighted projective space, is connected. This is achieved by exploiting techniques of toric geometry and the construction of Batyrev that relate Calabi-Yau manifolds to reflexive polyhedra. Taken together with the previously known fact that the moduli space of all CICY's is connected, and is moreover connected to the moduli space of the present class of Calabi-Yau manifolds (since the quintic threefold P_4[5] is both CICY and a hypersurface in a weighted P_4, this strongly suggests that the moduli space of all simply connected Calabi-Yau manifolds is connected. It is of interest that singular Calabi-Yau manifolds corresponding to the points in which the moduli spaces meet are often, for the present class, more singular than the conifolds that connect the moduli spaces of CICY's.
TL;DR: In this article, the authors calculate correlation functions of topological sigma model (A-model) on Calabi-Yau hypersurfaces in $CP^{N-1}$ using torus action method.
Abstract: We calculate correlation functions of topological sigma model (A-model) on Calabi-Yau hypersurfaces in $CP^{N-1}$ using torus action method. We also obtain path-integral represention of free energy of the theory coupled to gravity.
TL;DR: In this paper, a class of superstring models compactified in the 3-generation Calabi-Yau manifold of Tian and Yau is studied. But the model is highly nonminimal near the unification scale, and the predicted mass matrices have no simple symmetry properties.
TL;DR: In this paper, the B-model on the mirror pair of X2N−2(2, 2, …,2, 1, 1), which is an (n−2)-dimensional Calabi-Yau manifold and has two marginal operators, is presented.
Abstract: We calculate the B-model on the mirror pair of X2N−2(2, 2, …, 2, 1, 1), which is an (N−2)-dimensional Calabi-Yau manifold and has two marginal operators, i.e. h1,1(X2N−2(2, 2, …, 2, 1, 1))=2. In Ref. 1 we have discussed about mirror symmetry on XN(1, 1, …, 1) and its mirror pair. However, XN(1, 1, …, 1) had only one moduli. In this letter, we extend its methods to the case with a few moduli using toric geometry.
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TL;DR: A revised version with a number of corrections and refinements is presented in this article. But it does not address the problem of the lack of a detailed discussion of the authorship.
Abstract: A revised version with a number of corrections and refinements.
TL;DR: In this paper, the effect of curved two-dimensional space-time on Witten's N = 2 supersymmetric sigma models interpolating Calabi-Yau hypersurfaces to Landau-Ginzburg models is considered.
TL;DR: In this article, the general case of a type IIA string compactified on a Calabi-Yau manifold which has a heterotic dual description was considered and it was shown that the nonabelian gauge symmetries which can appear nonperturbatively in the type II string but which are understood perturbatively by the heterotic string are purely a result of string-string duality in six dimensions.
Abstract: We consider the general case of a type IIA string compactified on a Calabi-Yau manifold which has a heterotic dual description. It is shown that the nonabelian gauge symmetries which can appear nonperturbatively in the type II string but which are understood perturbatively in the heterotic string are purely a result of string-string duality in six dimensions. We illustrate this with some examples.