Showing papers on "Calabi–Yau manifold published in 1997"
TL;DR: In this article, the authors discuss necessary conditions for existence of non-trivial renormalization group fixed points and find all possible gauge groups and matter content which satisfy them, and explore connections between aspects of the gauge theory and Calabi-Yau geometry.
634 citations
TL;DR: In this paper, the authors discuss necessary conditions for the existence of nontrivial renormalization group fixed points and find all possible gauge groups and matter content that satisfy them, and explore connections between aspects of the gauge theory and Calabi-Yau geometry.
Abstract: We discuss five-dimensional supersymmetric gauge theories. An anomaly renders some theories inconsistent and others consistent only upon including a Wess-Zumino type Chern-Simons term. We discuss some necessary conditions for existence of nontrivial renormalization group fixed points and find all possible gauge groups and matter content which satisfy them. In some cases, the existence of these fixed points can be inferred from string duality considerations. In other cases, they arise from M-theory on Calabi-Yau threefolds. We explore connections between aspects of the gauge theory and Calabi-Yau geometry. A consequence of our classification of field theories with nontrivial fixed points is a fairly complete classification of a class of singularities of Calabi-Yau threefolds which generalize the ``del Pezzo contractions'' and occur at higher codimension walls of the K\"{a}hler cone.
380 citations
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TL;DR: These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years as discussed by the authors, including new geometric features of string theory which occur even at the classical level as well as those which require nonperturbative effects.
Abstract: These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments discussed include new geometric features of string theory which occur even at the classical level as well as those which require non-perturbative effects. These lecture notes are based on an evolving set of lectures presented at a number of schools but most closely follow a series of seven lectures given at the TASI-96 summer school on Strings, Fields and Duality.
260 citations
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01 Jul 1997
TL;DR: In this paper, the implications of R4 couplings in M-theory when compactified on Calabi-Yau (CY) manifolds are discussed, and a universal nonperturbative correction to the type IIB hyper-metric is discussed.
Abstract: Abstract We discuss several implications of R4 couplings in M-theory when compactified on Calabi-Yau (CY) manifolds. In particular, these couplings can be predicted by supersymmetry from the mixed gauge-gravitational Chem-Simons couplings in five dimensions and are related to the one-loop holomorphic anomaly in four-dimensional N = 2 theories. We find a new contribution to the Einstein term in five dimensions proportional to the Euler number of the internal CY threefold, which corresponds to a one-loop correction of the hypermultiplet geometry. This correction is reproduced by a direct computation in type 11 string theories. Finally, we discuss a universal non-perturbative correction to the type IIB hyper-metric.
243 citations
TL;DR: In this paper, the authors investigated topological properties of Calabi-Yau fourfolds and considered a wide class of explicit constructions in weighted projective spaces and more generally, toric varieties.
Abstract: We investigate topological properties of Calabi-Yau fourfolds and consider a wide class of explicit constructions in weighted projective spaces and, more generally, toric varieties. Divisors which lead to a non-perturbative superpotential in the effective theory have a very simple description in the toric construction. Relevant properties of them follow just by counting lattice points and can be also used to construct examples with negative Euler number. We study nets of transitions between cases with generically smooth elliptic fibres and cases with ADE gauge symmetries in the N=1 theory due to degenerations of the fibre over codimension one loci in the base. Finally we investigate the quantum cohomology ring of this fourfolds using Frobenius algebras.
223 citations
TL;DR: In this article, the singularities in the moduli space of Calabi-Yau spaces are modified by world-sheet instantons to singularities of F-theory compactifications to eight dimensions.
210 citations
TL;DR: In this paper, the implications of R4 couplings in M-theory when compactified on Calabi-Yau (CY) manifolds were discussed and a universal nonperturbative correction to the type IIB hyper-metric was discussed.
208 citations
CERN1
TL;DR: In this article, the authors studied aspects of Calabi-Yau four-folds as compactification manifolds of F-theory, using mirror symmetry of toric hypersurfaces.
155 citations
TL;DR: In this article, the authors studied F-theory compactified on elliptic Calabi-Yau threefolds that are realized as hypersurfaces in toric varieties, and found a large number of examples where the gauge group is not a subgroup of E 8 × E 8, but rather, is much bigger (with rank as high as 296).
152 citations
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TL;DR: In this paper, the microscopic entropy of certain 4 and 5 dimensional extermal black holes which arise for compactification of M-theory and type IIA on Calabi-Yau 3-folds was computed.
Abstract: We compute the microscopic entropy of certain 4 and 5 dimensional extermal black holes which arise for compactification of M-theory and type IIA on Calabi-Yau 3-folds. The results agree with macroscopic predictions, including some subleading terms. The macroscopic entropy in the 5 dimensional case predicts a surprising growth in the cohomology of moduli space of holomorphic curves in Calabi-Yau threefolds which we verify in the case of elliptic threefolds.
TL;DR: The Weil-Petersson metric on the Teichmuller space of compact Riemann surfaces is a Kahler metric, which is complete only in the case of elliptic curves as mentioned in this paper.
Abstract: The classical Weil-Petersson metric on the Teichmuller space of compact Riemann surfaces is a Kahler metric, which is complete only in the case of elliptic curves [Wo]. It has a natural generalization to the deformation spaces of higher dimansional polarized Kahler-Einstein manifolds. It is still Kahler, and in the case of abelian varieties and K3 surfaces, the Weil-Petersson metric turns out to coincide with the Bergman metric of the Hermitian symmetric period domain, hence is in fact “complete” Kahler-Einstein [Sc]. The completeness is an important property for differential geometric reason. Motivated by the above examples, one may naively think that the completeness of the Weil-Petersson metric still holds true for general Calabi-Yau manifolds (compact Kahler manifolds with trivial canonical bundle). However, explicit calculation done by physicists (eg. Candelas et al. [Ca] for some special nodal degenerations of Calabi-Yau 3-folds) indicated that this may not always be the case. The notion of completeness depends on the precise definition the “moduli space”. However, through our analysis, it would become clear that the Weil-Petersson metric is in general incomplete if one sticks
TL;DR: In this paper, the authors prove some version of Morrison's conjecture on the cone of divisors for Calabi-Yau fiber spaces with non-trivial base pace whose total space is 3-dimensional.
Abstract: We prove some version of Morrison's conjecture on the cone of divisors for Calabi-Yau fiber spaces with non-trivial base pace whose total space is 3-dimensional.
TL;DR: In this article, the authors studied the limits of four-dimensional type II Calabi-Yau compactifications with vanishing 4-cycle singularities, which are dual to T 2 compactifications of the six-dimensional non-critical string with E 8 symmetry.
TL;DR: In this paper, the authors considered mirror symmetry for Calabi-Yau threefolds of the type considered by Voisin and Borcea, of the form SxE/involution where S is a K3 surface with involution, and E is an elliptic curve.
Abstract: We give an example of the recent proposed mirror construction of Strominger, Yau and Zaslow in ``Mirror Symmetry is T-duality,'' hep-th/9606040. The paper first considers mirror symmetry for K3 surfaces in light of this construction. We then consider the example of mirror symmetry for Calabi-Yau threefolds of the type considered by Voisin and Borcea, of the form SxE/involution where S is a K3 surface with involution, and E is an elliptic curve. We show how dualizing a family of special Lagrangian real 3-tori does actually produce the mirrors in these examples.
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TL;DR: In this paper, the authors prove some version of Morrison's conjecture on the cone of divisors for Calabi-Yau fiber spaces with non-trivial base pace whose total space is 3-dimensional.
Abstract: We prove some version of Morrison's conjecture on the cone of divisors for Calabi-Yau fiber spaces with non-trivial base pace whose total space is 3-dimensional.
Dissertation•
01 Jan 1997
TL;DR: In this article, the authors studied complex analogues on Calabi-Yau manifolds of gauge theories on low dimensional real manifolds and defined a holomorphic analogue of the Casson invariant, counting coherent sheaves on a Calabi Yau 3-fold.
Abstract: We study complex analogues on Calabi-Yau manifolds of gauge theories on low dimensional real manifolds. In particular we define a holomorphic analogue of the Casson invariant, counting coherent sheaves on a Calabi-Yau 3-fold.
TL;DR: In this paper, it was shown that the Dynkin diagrams of nonabelian gauge groups occurring in type IIA and F-theory can be read off from the polyhedron Δ∗ that provides the toric description of the Calabi-Yau manifold used for compactification.
TL;DR: In this paper, the smoothability of Calabi-Yau threefold with canonical singularities was studied, and it was shown that X' is smoothable if f:X'->X is a contraction of a divisor to a curve.
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
TL;DR: In this paper, it was shown that all Calabi-Yau 3-folds are connected among themselves and to the web of CICYs, which almost completes the proof of connectedness for toric CalabiYau hypersurfaces.
TL;DR: In this paper, it was shown that divisors contributing to the superpotential are always "exceptional" (in some sense) for the Calabi-Yau 4-fold X, also in M-theory.
Abstract: Each smooth elliptic Calabi-Yau 4-fold determines both a three-dimensional physical theory (a compactification of ``M-theory'') and a four-dimensional physical theory (using the ``F-theory'' construction). A key issue in both theories is the calculation of the ``superpotential''of the theory. We propose a systematic approach to identify these divisors, and derive some criteria to determine whether a given divisor indeed contributes. We then apply our techniques in explicit examples, in particular, when the base B of the elliptic fibration is a toric variety or a Fano 3-fold. When B is Fano, we show how divisors contributing to the superpotential are always "exceptional" (in some sense) for the Calabi-Yau 4-fold X. This naturally leads to certain transitions of X, that is birational transformations to a singular model (where the image of D no longer contributes) as well as certain smoothings of the singular model. If a smoothing exists, then the Hodge numbers change. We speculate that divisors contributing to the superpotential are always "exceptional" (in some sense) for X, also in M-theory. In fact we show that this is a consequence of the (log)-minimal model algorithm in dimension 4, which is still conjectural in its generality, but it has been worked out in various cases, among which toric varieties.
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.
KEK1
TL;DR: In this paper, the Fayet-Iliopoulos parameters on the world volume of the type IIB D1-brane at the singular point of a Calabi-Yau fourfold were investigated.
Abstract: We investigate a (0,2) gauge theory realized on the world volume of the type IIB D1-brane at the singular point of a Calabi-Yau fourfold. It is argued that the gauge anomaly can be canceled via coupling to the R-R chiral bosons in bulk IIB string. We find that for a generic choice of the Fayet-Iliopoulos parameters on the world volume, the Higgs moduli space is a smooth fourfold birational to the original Calabi-Yau fourfold, but is not necessarily a Calabi-Yau manifold.
TL;DR: In this paper, splitting-type phase transitions between Calabi-Yau fourfolds are considered, which generalize previously known types of conifold transitions between three-folds.
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TL;DR: In this article, the moduli theory of Calabi-Yau threefolds was investigated, and Griffiths' work on the period map was used to derive finiteness results.
Abstract: We investigate the moduli theory of Calabi--Yau threefolds, and using Griffiths' work on the period map, we derive some finiteness results. In particular, we confirm a prediction of Morrison's Cone Conjecture.
TL;DR: In this paper, the authors constructed a Calabi-Yau manifold corresponding to F-theory vacua dual to E 8 × E 8 heterotic strings compactified to six dimensions on K 3 surfaces with non-semisimple gauge backgrounds.
TL;DR: In this article, the moduli of the internal Calabi-Yau space vary over four-dimensional space time, and the corresponding solutions of 4D N = 2 supergravity are given by charged, extremal BPS black hole configurations with non-constant scalar field values.
Abstract: In this paper we discuss compactifications of type II superstrings where the moduli of the internal Calabi-Yau space vary over four-dimensional space time. The corresponding solutions of four-dimensional N=2 supergravity are given by charged, extremal BPS black hole configurations with non-constant scalar field values. In particular we investigate the behaviour of our solutions near those points in the Calabi-Yau moduli space where some internal cycles collapse and topology change (flop transitions, conifold transitions) can take place. The singular loci in the internal space are related to special points in the uncompactified space. The phase transition can happen either at spatial infinity (for positive charges) or on spheres (with at least one negative charge). The corresponding BPS configuration has zero ADM mass and can be regarded as a domain wall that separates topologically different vacua of the theory.
TL;DR: In this paper, a simple hypothesis about the degrees of freedom of intersecting branes was used to find a counting argument that reproduces the entropy of a class of BPS black holes of type IIA string theory on general Calabi Yau.
01 Jul 1997
TL;DR: In this article, the authors review several aspects of heterotic, type II, F-theory, and Mtheory compactifications on Calabi-Yau three-folds and fourfolds.
Abstract: We review several aspects of heterotic, type II, F-theory, and M-theory compactifications on Calabi-Yau three-folds and fourfolds. In the context of dualities we focus on the heterotic gauge structure determined by the various types of fibration relevant in the framework of heterotic/type II duality in D=4 as well as 4D F-theory. We also consider transitions between Calabi-Yau manifolds in both three and four dimensions and review some of the consequences for the behavior of the superpotential.
TL;DR: In this article, the authors show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of rational curves on complete intersection Calabi Yau 3 -folds in Grassmannians.
Abstract: In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of rational curves on complete intersection Calabi-Yau 3-folds in Grassmannians. Using a natural degeneration of Grassmannians $G(k,n)$ to some Gorenstein toric Fano varieties $P(k,n)$ with conifolds singularities which was recently described by Sturmfels, we suggest an explicit mirror construction for Calabi-Yau complete intersections $X \subset G(k,n)$ of arbitrary dimension. Our mirror construction is consistent with the formula for the Lax operator conjectured by Eguchi, Hori and Xiong for gravitational quantum cohomology of Grassmannians.