Built on

I. Antoniadis, Y. Chen and G. K. Leontaris, Logarithmic loop corrections, moduli stabilisation and de Sitter vacua in string theory , JHEP 01
Original
1909
Earlier work this paper cites.
M. Demirtas, M. Kim, L. Mcallister and J. Moritz, Vacua with Small Flux Superpotential , Phys. Rev. Lett. 124
Original
1912
Earlier work this paper cites.
K. Bobkov, V. Braun, P. Kumar and S. Raby, Stabilizing All Kahler Moduli in Type IIB Orientifolds , JHEP 12
Original
1982
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. 109
1987
Earlier work this paper cites.
P. Candelas, A. M. Dale, C. A. Lutken and R. Schimmrigk, Complete Intersection Calabi-Yau Manifolds , Nucl. Phys. B 298
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. 6
1989
Earlier work this paper cites.
K. Oguiso, On Algebraic Fiber Space Structures on a Calabi-Yau 3-Fold , International Journal of Mathematics 04
1993
Earlier work this paper cites.
P. Candelas, X. De La Ossa, A. Font, S. H. Katz and D. R. Morrison, Mirror symmetry for two parameter models. 1. , Nucl. Phys. B 416
1994
Earlier work this paper cites.
V. V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties , J. Alg. Geom. 3
1994
Earlier work this paper cites.
P. Candelas, A. Font, S. H. Katz and D. R. Morrison, Mirror symmetry for two parameter models. 2. , Nucl. Phys. B 429
1994
Earlier work this paper cites.
S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces , Nucl. Phys. B 433
1995
Earlier work this paper cites.
E. Witten, Nonperturbative superpotentials in string theory , Nucl. Phys. B 474
1996
Earlier work this paper cites.
M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four-dimensions , Adv. Theor. Math. Phys. 4
2000
Earlier work this paper cites.
F. Carta, J. Moritz and A. Westphal, A landscape of orientifold vacua , JHEP 05
Original
2003
Earlier work this paper cites.
S. Kachru, R. Kallosh, A. D. Linde and S. P. Trivedi, De Sitter vacua in string theory , Phys. Rev. D68
2003
Earlier work this paper cites.
M. R. Douglas, The Statistics of string / M theory vacua , JHEP 05
2003
Earlier work this paper cites.
M. Kreuzer and H. Skarke, PALP: A Package for analyzing lattice polytopes with applications to toric geometry , Comput. Phys. Commun. 157
2004
Earlier work this paper cites.
S. AbdusSalam, S. Abel, M. Cicoli, F. Quevedo and P. Shukla, A systematic approach to Kähler moduli stabilisation , JHEP 08
Original
2005
Earlier work this paper cites.
V. Balasubramanian, P. Berglund, J. P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications , JHEP 03
2005
Earlier work this paper cites.
M. Berg, M. Haack and B. Kors, String loop corrections to Kahler potentials in orientifolds , JHEP 11
2005
Earlier work this paper cites.
G. von Gersdorff and A. Hebecker, Kahler corrections for the volume modulus of flux compactifications , Phys. Lett. B 624
2005
Earlier work this paper cites.
M. Berg, M. Haack and E. Pajer, Jumping Through Loops: On Soft Terms from Large Volume Compactifications , JHEP 09
Original
2007
Earlier work this paper cites.
M. Demirtas, L. McAllister and A. Rios-Tascon, Bounding the Kreuzer-Skarke Landscape , Fortsch. Phys. 68
Original
2008
Earlier work this paper cites.
M. Cicoli, J. P. Conlon and F. Quevedo, Systematics of String Loop Corrections in Type IIB Calabi-Yau Flux Compactifications , JHEP 01
Original
2008
Earlier work this paper cites.
R. Blumenhagen, V. Braun, T. W. Grimm and T. Weigand, GUTs in Type IIB Orientifold Compactifications , Nucl.Phys. B815
Original
2009
Earlier work this paper cites.

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2022

Classifying divisor topologies for string phenomenology

Shukla, Pramod

Understand

In this article we present a pheno-inspired classification for the divisor topologies of the favorable Calabi Yau (CY) threefolds with $1 \leq h^{1,1}(CY) \leq 5$ arising from the four-dimensional reflexive polytopes of the Kreuzer-Skarke database.

Based on some empirical observations we conjecture that the topologies of the so-called coordinate divisors can be classified into two categories: (i).
$\chi_{_h}(D) \geq 1$ with Hodge numbers given by $\{h^{0,0} = 1, \, h^{1,0} = 0, \, h^{2,0} = \chi_{_h}(D) -1, \, h^{1,1} = \chi(D) - 2 \chi_{_h}(D) \}$ and (ii).
$\chi_{_h}(D) \leq 1$ with Hodge numbers given by $\{h^{0,0} = 1, \, h^{1,0} = 1 - \chi_{_h}(D), \, h^{2,0} = 0, \, h^{1,1} = \chi(D) + 2 - 4 \chi_{_h}(D)\}$, where $\chi_{_h}(D)$ denotes the Arithmetic genus while $\chi(D)$ denotes the Euler characteristic of the divisor $D$.

Built on

I. Antoniadis, Y. Chen and G. K. Leontaris, Logarithmic loop corrections, moduli stabilisation and de Sitter vacua in string theory , JHEP 01
Original
1909
Earlier work this paper cites.
M. Demirtas, M. Kim, L. Mcallister and J. Moritz, Vacua with Small Flux Superpotential , Phys. Rev. Lett. 124
Original
1912
Earlier work this paper cites.
K. Bobkov, V. Braun, P. Kumar and S. Raby, Stabilizing All Kahler Moduli in Type IIB Orientifolds , JHEP 12
Original
1982
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. 109
1987
Earlier work this paper cites.
P. Candelas, A. M. Dale, C. A. Lutken and R. Schimmrigk, Complete Intersection Calabi-Yau Manifolds , Nucl. Phys. B 298
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. 6
1989
Earlier work this paper cites.
K. Oguiso, On Algebraic Fiber Space Structures on a Calabi-Yau 3-Fold , International Journal of Mathematics 04
1993
Earlier work this paper cites.
P. Candelas, X. De La Ossa, A. Font, S. H. Katz and D. R. Morrison, Mirror symmetry for two parameter models. 1. , Nucl. Phys. B 416
1994
Earlier work this paper cites.
V. V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties , J. Alg. Geom. 3
1994
Earlier work this paper cites.
P. Candelas, A. Font, S. H. Katz and D. R. Morrison, Mirror symmetry for two parameter models. 2. , Nucl. Phys. B 429
1994
Earlier work this paper cites.
S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces , Nucl. Phys. B 433
1995
Earlier work this paper cites.
E. Witten, Nonperturbative superpotentials in string theory , Nucl. Phys. B 474
1996
Earlier work this paper cites.
M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four-dimensions , Adv. Theor. Math. Phys. 4
2000
Earlier work this paper cites.
F. Carta, J. Moritz and A. Westphal, A landscape of orientifold vacua , JHEP 05
Original
2003
Earlier work this paper cites.
S. Kachru, R. Kallosh, A. D. Linde and S. P. Trivedi, De Sitter vacua in string theory , Phys. Rev. D68
2003
Earlier work this paper cites.
M. R. Douglas, The Statistics of string / M theory vacua , JHEP 05
2003
Earlier work this paper cites.
M. Kreuzer and H. Skarke, PALP: A Package for analyzing lattice polytopes with applications to toric geometry , Comput. Phys. Commun. 157
2004
Earlier work this paper cites.
S. AbdusSalam, S. Abel, M. Cicoli, F. Quevedo and P. Shukla, A systematic approach to Kähler moduli stabilisation , JHEP 08
Original
2005
Earlier work this paper cites.
V. Balasubramanian, P. Berglund, J. P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications , JHEP 03
2005
Earlier work this paper cites.
M. Berg, M. Haack and B. Kors, String loop corrections to Kahler potentials in orientifolds , JHEP 11
2005
Earlier work this paper cites.
G. von Gersdorff and A. Hebecker, Kahler corrections for the volume modulus of flux compactifications , Phys. Lett. B 624
2005
Earlier work this paper cites.
M. Berg, M. Haack and E. Pajer, Jumping Through Loops: On Soft Terms from Large Volume Compactifications , JHEP 09
Original
2007
Earlier work this paper cites.
M. Demirtas, L. McAllister and A. Rios-Tascon, Bounding the Kreuzer-Skarke Landscape , Fortsch. Phys. 68
Original
2008
Earlier work this paper cites.
M. Cicoli, J. P. Conlon and F. Quevedo, Systematics of String Loop Corrections in Type IIB Calabi-Yau Flux Compactifications , JHEP 01
Original
2008
Earlier work this paper cites.
R. Blumenhagen, V. Braun, T. W. Grimm and T. Weigand, GUTs in Type IIB Orientifold Compactifications , Nucl.Phys. B815
Original
2009
Earlier work this paper cites.