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## A Comprehensive Scan for Heterotic SU(5) GUT models

### Citations

617 |
On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation,
- Yau
- 1978
(Show Context)
Citation Context ...holomorphic prefactor, whose computation requires the explicit knowledge of the metric on X and the gauge connection on the vector bundle V . For the case when X is a Calabi-Yau manifold, Yau’s proof =-=[39]-=- guarantees the existence of a Ricci-flat metric, while for poly-stable vector bundles on Calabi-Yau manifolds, the Donaldson-Uhlenbeck-Yau theorem [40,41] guarantees the existence of a Hermitian Yang... |

408 |
The geometry of moduli spaces of sheaves,
- Huybrechts, Lehn
- 2010
(Show Context)
Citation Context ...hler cone (tr > 0 ∀r). Finally, we note that for slope(poly)-stable bundles on a Calabi-Yau threefold there is a positivity condition on the second Chern class, given by the so-called Bogomolov bound =-=[55]-=-. For SU(n) bundles this takes the simple form ∫ X c2(V ) ∧ J ≥ 0 (4.6) and J is any Kähler form for which V is poly-stable. 4.3 Constraints from the GUT Spectrum The SU(5) × S ( U(1)5 ) GUT spectrum... |

288 |
On the existence of Hermitian–Yang–Mills connections in stable vector bundles.
- Uhlenbeck, Yau
- 1986
(Show Context)
Citation Context ...se when X is a Calabi-Yau manifold, Yau’s proof [39] guarantees the existence of a Ricci-flat metric, while for poly-stable vector bundles on Calabi-Yau manifolds, the Donaldson-Uhlenbeck-Yau theorem =-=[40,41]-=- guarantees the existence of a Hermitian Yang-Mills connection. However, except in very special cases, these quantities are not known analytically. So far, one can approach this differential geometric... |

204 |
Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles,
- Donaldson
- 1985
(Show Context)
Citation Context ...se when X is a Calabi-Yau manifold, Yau’s proof [39] guarantees the existence of a Ricci-flat metric, while for poly-stable vector bundles on Calabi-Yau manifolds, the Donaldson-Uhlenbeck-Yau theorem =-=[40,41]-=- guarantees the existence of a Hermitian Yang-Mills connection. However, except in very special cases, these quantities are not known analytically. So far, one can approach this differential geometric... |

164 |
Algebraic surfaces and holomorphic vector bundles,
- Friedman
- 1998
(Show Context)
Citation Context ...s 3. Instead, our starting point is an explicit formal construction of a rank n holomorphic vector bundle (for example a sum of line bundles, or a bundle constructed via a monad [18], or by extension =-=[61]-=-). The question now becomes, can we be sure that the given collection of vector bundles really arose from an H-valued principle bundle? Suppose, for example, that we consider a holomorphic rank 3 vect... |

86 | The exact MSSM spectrum from string theory, JHEP 0605 - Braun, He, et al. - 2006 |

72 | Supersymmetric standard model from the heterotic - Buchmuller, Hamaguchi, et al. |

67 | Heterotic string theory. 1. The free heterotic string - Gross, Harvey, et al. - 1985 |

61 | Heterotic GUT and standard model vacua from simply connected Calabi-Yau manifolds - Blumenhagen, Moster, et al. |

44 | Heterotic compactification, an algorithmic approach
- Anderson, He, et al.
(Show Context)
Citation Context ...relevant vector bundles 3. Instead, our starting point is an explicit formal construction of a rank n holomorphic vector bundle (for example a sum of line bundles, or a bundle constructed via a monad =-=[18]-=-, or by extension [61]). The question now becomes, can we be sure that the given collection of vector bundles really arose from an H-valued principle bundle? Suppose, for example, that we consider a h... |

42 | Heterotic string theory. 2. The interacting heterotic string - Gross, Harvey, et al. - 1986 |

41 | A standard model from the E(8) x E(8) heterotic superstring - Braun, He, et al. - 2005 |

35 | Heterotic mini-landscape (II): completing the search for MSSM vacua in a Z6 orbifold”, Phys - Lebedev, Nilles, et al. |

34 | Exploring Positive Monad Bundles And A New Heterotic Standard Model - Anderson, Gray, et al. |

30 | An SU(5) heterotic standard model,” - Bouchard, Donagi - 2006 |

25 | Some Three Generation (0,2) Calabi-Yau Models,” - Kachru - 1995 |

23 | A three-generation Calabi-Yau manifold with small Hodge numbers,” Fortschritte der Physik, - Braun, Candelas, et al. - 2010 |

23 | Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic,” hep-th/0606261 - Douglas, Karp, et al. |

22 | New Calabi-Yau Manifolds with Small Hodge Numbers, ArXiv e-prints
- Candelas, Davies
- 2008
(Show Context)
Citation Context ... features of the CICY class of manifolds. In the first place, there exists a systematic classification of all linearly realised freely acting discrete symmetries on the CICY manifolds in the database =-=[52, 53]-=-. More accurately, Braun’s classification [53] provides a list of all such symmetries which descend from a linearly acting symmetry on the ambient space. Furthermore, a given Calabi-Yau manifold can f... |

19 | Superstring standard model from Z12-I orbifold compactification with and without exotics, and effective R- parity,” JHEP 06 - Kim, Kim, et al. - 2007 |

16 |
Complex geometry. An introduction, Universitext
- Huybrechts
- 2005
(Show Context)
Citation Context ...ust be a subgroup of SU(5), SO(5) or Sp(4) (see Appendix A). The latter two structure groups are possible for a rank 5 vector bundle only if V5 admits either a real or symplectic fiber structure (see =-=[49, 50]-=- and (A.7)), in the form of a vector bundle isomorphism, φ : V → V ∗. Since ⊕ a La is an odd sum of 5 line bundles, such an isomorphism is possible if and only if La = OX for at least one a. To avoid ... |

14 |
A Three Generation Superstring Model. 2. Symmetry Breaking And The Low-Energy Theory,” Nucl. Phys. B292
- Greene, Kirklin, et al.
- 1987
(Show Context)
Citation Context ...he early days of the subject researchers largely concentrated on small deviations from the “standard embedding”, where the gauge bundle was taken to be a holomorphic deformation of the tangent bundle =-=[5, 6]-=-. Such work has been continued to the current day with the first exact MSSM being produced from such an approach relatively recently [8]. In the 1990’s and later more general poly-stable holomorphic v... |

12 | et al., “The Heterotic Road to the MSSM with R parity,” Phys - Lebedev |

11 |
Three generation superstring model. 1. Compactification and discrete symmetries. Nucl. Phys
- Greene, Kirklin, et al.
- 1986
(Show Context)
Citation Context ...he early days of the subject researchers largely concentrated on small deviations from the “standard embedding”, where the gauge bundle was taken to be a holomorphic deformation of the tangent bundle =-=[5, 6]-=-. Such work has been continued to the current day with the first exact MSSM being produced from such an approach relatively recently [8]. In the 1990’s and later more general poly-stable holomorphic v... |

11 | Stabilizing All Geometric Moduli - Anderson, Gray, et al. |

11 | Semistable principal G-bundles in positive characteristic
- Langer
(Show Context)
Citation Context ...e values for c2(V ). Moreover, for an SU(n) vector bundle which is semistable somewhere in the Kähler cone, it is known that there can be only finitely many values possible for the third Chern class =-=[56, 57]-=-. Moreover for fixed topology (that is, fixed total Chern class) the moduli space of semi-stable sheaves on a Calabi-Yau threefold is known (by algebraicity of the family [55, 56]) to have only finite... |

7 | Permutation orbifolds of heterotic Gepner models, Nuclear Phys - Maio, Schellekens |

6 | A Heterotic standard model,” Phys.Lett. B618 - Braun, He, et al. - 2005 |

6 |
On Free Quotients of Complete Intersection
- Braun
(Show Context)
Citation Context ... features of the CICY class of manifolds. In the first place, there exists a systematic classification of all linearly realised freely acting discrete symmetries on the CICY manifolds in the database =-=[52, 53]-=-. More accurately, Braun’s classification [53] provides a list of all such symmetries which descend from a linearly acting symmetry on the ambient space. Furthermore, a given Calabi-Yau manifold can f... |

4 |
On boundedness of torsion free sheaves
- Maruyama
- 1981
(Show Context)
Citation Context ...e values for c2(V ). Moreover, for an SU(n) vector bundle which is semistable somewhere in the Kähler cone, it is known that there can be only finitely many values possible for the third Chern class =-=[56, 57]-=-. Moreover for fixed topology (that is, fixed total Chern class) the moduli space of semi-stable sheaves on a Calabi-Yau threefold is known (by algebraicity of the family [55, 56]) to have only finite... |

3 |
Holomorphic bundles over elliptic manifolds”, Lecture notes at the School on Algebraic Geometry
- Morgan
- 1999
(Show Context)
Citation Context ...ust be a subgroup of SU(5), SO(5) or Sp(4) (see Appendix A). The latter two structure groups are possible for a rank 5 vector bundle only if V5 admits either a real or symplectic fiber structure (see =-=[49, 50]-=- and (A.7)), in the form of a vector bundle isomorphism, φ : V → V ∗. Since ⊕ a La is an odd sum of 5 line bundles, such an isomorphism is possible if and only if La = OX for at least one a. To avoid ... |

2 | Asymmetric Gepner Models II: Heterotic Weight Lifting”, NIKHEF/2010-30, IFF-FM-2010/02, to appear. Nr. Name Current Order Gauge group Grp. CFT 0 - Gato-Rivera, Schellekens |

1 | et al., “Investigation of Quasi-Realistic Heterotic String Models with Reduced Higgs Spectrum,” Eur.Phys.J. C71 - Cleaver, Faraggi, et al. - 2011 |