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This is a short review of recent constructions of new Calabi-Yau threefolds with small Hodge numbers and/or non-trivial fundamental group, which are of particular interest for model-building in the context of heterotic string theory.
P. Candelas, P. S. Green, and T. Hubsch, “Finite Distances Between Distinct Calabi-Yau Vacua: (Other Worlds Are Just Around The Corner),” Phys. Rev. Lett
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R. Hartshorne, Algebraic Geometry · 1977
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P. Candelas, G. T. Horowitz, A. Strominger, and E. Witten, “Vacuum Configurations for Superstrings,” Nucl.Phys
1985
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S.-T. Yau, “Compact three-dimensional Kähler manifolds with zero Ricci curvature,”. In *Argonne/Chicago 1985, Proceedings, Anomalies, Geometry, Topology*, 395-406
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A. Strominger and E. Witten, “New manifolds for superstring compactification,” Commun. Math. Phys
1985
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E. Witten, “New Issues in Manifolds of SU(3) Holonomy,” Nucl. Phys
1986
Earlier work this paper cites.
P. Green and T. Hubsch, “Calabi-Yau Manifolds As Complete Intersections In Products Of Complex Projective Spaces,” Commun.Math.Phys
1987
Earlier work this paper cites.
R. Schimmrigk, “A new construction of a three generation Calabi-Yau manifold,” Phys. Lett
1987
Earlier work this paper cites.
M. Reid, “The moduli space of 3-folds with K=0 may nevertheless be irreducible,” Math. Ann
1987
Earlier work this paper cites.
P. Candelas, A. M. Dale, C. A. Lutken, and R. Schimmrigk, “Complete Intersection Calabi-Yau Manifolds,” Nucl. Phys
1988
Earlier work this paper cites.
P. Candelas, C. A. Lutken, and R. Schimmrigk, “Complete Intersection Calabi-Yau Manifolds. 2. Three Generation Manifolds,” Nucl. Phys
1988
Earlier work this paper cites.
P. S. Green and T. Hubsch, “Connecting moduli spaces of Calabi-Yau threefolds,” Commun. Math. Phys
1988
Earlier work this paper cites.
P. S. Green and T. Hubsch, “Phase transitions among (many of) Calabi-Yau compactifications,” Phys. Rev. Lett
1988
Earlier work this paper cites.
P. S. Green, T. Hubsch, and C. A. Lutken, “All Hodge Numbers of All Complete Intersection Calabi-Yau Manifolds,” Class. Quant. Grav
1989
Earlier work this paper cites.
B. McInnes, “Group theoretic aspects of the Hosotani mechanism,” J. Phys
1989
Cited alongside, same era.
P. Candelas, P. S. Green, and T. Hubsch, “Rolling Among Calabi-Yau Vacua,” Nucl. Phys
1990
Cited alongside, same era.
P. Candelas and X. C. de la Ossa, “Comments on Conifolds,” Nucl. Phys
1990
Cited alongside, same era.
A. Strominger, “Massless black holes and conifolds in string theory,” Nucl.Phys
1995
Cited alongside, same era.
B. R. Greene, D. R. Morrison, and A. Strominger, “Black hole condensation and the unification of string vacua,” Nucl. Phys
1995
Cited alongside, same era.
M. Kreuzer and H. Skarke, “On the Classification of Reflexive Polyhedra,” Commun. Math. Phys
V. Bouchard, M. Cvetic, and R. Donagi, “Tri-linear couplings in an heterotic minimal supersymmetric standard model,” Nucl. Phys
2006
Later among the works it cites.
V. Braun, M. Kreuzer, B. A. Ovrut, and E. Scheidegger, “Worldsheet instantons and torsion curves. Part A: Direct computation,” JHEP
2007
Later among the works it cites.
2007
Later among the works it cites.
2008
Later among the works it cites.
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1997
Cited alongside, same era.
A. Beauville, “A Calabi-Yau Threefold with Non-Abelian Fundamental Group,” alg-geom/9502003 . In: New trends in algebraic geometry, 13, LMS Lect. Note Ser. 264, CUP, Cambridge, 1999
1999
Cited alongside, same era.
M. Gross and S. Popescu, “Calabi-Yau Threefolds and Moduli of Abelian Surfaces I,” Compositio Mathematica
2001
Cited alongside, same era.
M. Kreuzer and H. Skarke, “Complete classification of reflexive polyhedra in four-dimensions,” Adv.Theor.Math.Phys
2002
Cited alongside, same era.
Cambridge University Press, 2002
A. Hatcher, Algebraic Topology · 2002
Cited alongside, same era.
V. Braun, B. A. Ovrut, T. Pantev, and R. Reinbacher, “Elliptic Calabi-Yau threefolds with Z(3) x Z(3) Wilson lines,” JHEP
2004
Cited alongside, same era.
J. Li and S.-T. Yau, “The existence of supersymmetric string theory with torsion,” J.Differential Geom
2005
Cited alongside, same era.
2008
Later among the works it cites.
L. Borisov and Z. Hua, “On Calabi-Yau Threefolds with Large Nonabelian Fundamental Group,” Proc.Amer.Math.Soc
2008
Later among the works it cites.
2009
Later among the works it cites.
P. Candelas and R. Davies, “New Calabi-Yau Manifolds with Small Hodge Numbers,” Fortsch. Phys
2010
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2010
Later among the works it cites.
Wolfram Research, Inc., 2010
Wolfram Research, Inc., Mathematica, version 8.0 · 2010
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R. Davies, “Calabi-Yau Threefolds and Heterotic String Compactification,”. (2010), DPhil thesis, Oxford University, available at http://ora.ouls.ox.ac.uk/objects/uuid:be92aac5-6874-431e-95a0-ac61a88ee63d
2010
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2010
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A. Bak, V. Bouchard, and R. Donagi, “Exploring a new peak in the heterotic landscape,” JHEP
2010
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2011
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