Connecting moduli spaces of Calabi-Yau threefolds (original) (raw)
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On the global moduli of Calabi-Yau threefolds
arXiv (Cornell University), 2017
In this note we initiate a program to obtain global descriptions of Calabi-Yau moduli spaces, to calculate their Picard group, and to identify within that group the Hodge line bundle. We do this here for several Calabi-Yau's obtained in [DW09] as crepant resolutions of the orbifold quotient of the product of three elliptic curves. In particular we verify in these cases a recent claim of [GHKSST16] by noting that a power of the Hodge line bundle is trivial-even though in most of these cases the Picard group is infinite.
Standard-model bundles on non-simply connected Calabi-Yau threefolds
Journal of High Energy Physics, 2001
We give a proof of the existence of G = SU (5), stable holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds with fundamental group Z 2 . The bundles we construct have Euler characteristic 3 and an anomaly that can be absorbed by M-theory five-branes. Such bundles provide the basis for constructing the standard model in heterotic M-theory. They are also applicable to vacua of the weakly coupled heterotic string. We explicitly present a class of three family models with gauge group SU (3) C × SU (2) L × U (1) Y .
Heterotic string models on smooth Calabi-Yau threefolds
2013
and Prof. Graham Ross for their advice, inspiration and accurate knowledge shared with me in our conversations. I am grateful for the friendship and support of many of my colleagues (some of which have already graduated), especially of Maxime Gabella, Georgios Giasemidis, Michael Klaput, Cyril Matti, Challenger Mishra, Chuang Sun, Eirik Svanes and Lukas Witkowski. My DPhil studies and the present thesis wouldn't have been possible without the generous support received through the Bobby Berman scholarship offered by University College, Oxford and complemented by the STFC. The final year of my studies was partly supported through the College Lectureship offered by Brasenose College and I would like to thank Prof. Laura Herz and Prof. Jonathan Jones for giving me the chance to partake in this facet of Oxford's academic life. Last but not least, I would like to express my sincere gratitude towards my wife Carmen Maria for her constant love, friendship and support and for being my constitutive Other; to our children Elisabeta, Clara Theodora and Cristian for brightening up my life in countless ways; to my parents Carmen and Marin, my sister Alina and our extended family for their unconditional love and support. There are of course many more people who contributed to my becoming during these years and close friends whose advice, help and presence meant a lot for me. To all these people I am deeply grateful and indebted.
Towards refining the topological strings on compact Calabi-Yau 3-folds
Journal of High Energy Physics, 2021
We make a proposal for calculating refined Gopakumar-Vafa numbers (GVN) on elliptically fibered Calabi-Yau 3-folds based on refined holomorphic anomaly equations. The key examples are smooth elliptic fibrations over (almost) Fano surfaces. We include a detailed review of existing mathematical methods towards defining and calculating the (unrefined) Gopakumar-Vafa invariants (GVI) and the GVNs on compact Calabi-Yau 3-folds using moduli of stable sheaves, in a language that should be accessible to physicists. In particular, we discuss the dependence of the GVNs on the complex structure moduli and on the choice of an orientation. We calculate the GVNs in many instances and compare the B-model predictions with the geometric calculations. We also derive the modular anomaly equations from the holomorphic anomaly equations by analyzing the quasi-modular properties of the propagators. We speculate about the physical relevance of the mathematical choices that can be made for the orientation.
Heterotic strings on (K3 × T2)/ℤ3 and their dual Calabi-Yau threefolds
Journal of High Energy Physics
In this paper we study compactifications of the N = 2 heterotic E 8 × E 8 string on (K3 × T 2)/Z 3 with various gauge backgrounds and calculate the topological couplings in the effective supergravity action that arise from one-loop amplitudes. We then identify candidates for dual type IIA compactifications on Calabi-Yau threefolds and compare the heterotic results with the corresponding topological string amplitudes. We find that the dual Calabi-Yau geometries are K3 fibrations that are also genus one fibered with threesections. Moreover, we show that the intersection form on the polarization lattice of the K3 fibration has to be three times the intersection form on the Narain lattice Γ 1,1 .
Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities
Journal of High Energy Physics, 2019
We calculate the generating functions of BPS indices using their modular properties in Type II and M-theory compactifications on compact genus one fibered CY 3-folds with singular fibers and additional rational sections or just N -sections, in order to study string dualities in four and five dimensions as well as rigid limits in which gravity decouples. The generating functions are Jacobi-forms of Γ1(N) with the complexified fiber volume as modular parameter. The string coupling λ, or the ϵ± parameters in the rigid limit, as well as the masses of charged hypermultiplets and non-Abelian gauge bosons are elliptic parameters. To understand this structure, we show that specific auto-equivalences act on the category of topological B-branes on these geometries and generate an action of Γ1(N) on the stringy Kähler moduli space. We argue that these actions can always be expressed in terms of the generic Seidel-Thomas twist with respect to the 6-brane together with shifts of the B-field and ...
Calabi-Yau manifolds, discrete symmetries and string theory
2017
In this thesis we explore various aspects of Calabi-Yau (CY) manifolds and com- pactifications of the heterotic string over them. At first we focus on classifying symmetries and computing Hodge numbers of smooth CY quotients. Being non- simply connected, these quotients are an integral part of CY compactifications of the heterotic string, aimed at producing realistic string vacua. Discrete symmetries of such spaces that are generically present in the moduli space, are phenomenologically important since they may appear as symmetries of the associated low energy theory. We classify such symmetries for the class of smooth Complete Intersection CY (CICY) quotients, resulting in a large number of regular and R-symmetry examples. Our results strongly suggest that generic, non-freely acting symmetries for CY quotients arise relatively frequently. A large number of string derived Standard Models (SM) were recently obtained over this class of CY manifolds indicating that our results could be...
2019
In this paper we study compactifications of the calN=2{\cal N}=2calN=2 heterotic E8timesE8E_8\times E_8E_8timesE8 string on (K3timesT2)/mathbbZ3(K3\times T^2)/\mathbb{Z}_3(K3timesT2)/mathbbZ_3 with various gauge backgrounds and calculate the topological couplings in the effective supergravity action that arise from one-loop amplitudes. We then identify candidates for dual type IIA compactifications on Calabi-Yau threefolds and compare the heterotic results with the corresponding topological string amplitudes. We find that the dual Calabi-Yau geometries are K3K3K3 fibrations that are also genus one fibered with three-sections. Moreover, we show that the intersection form on the polarization lattice of the K3K3K3 fibration has to be three times the intersection form on the Narain lattice Gamma1,1\Gamma^{1,1}Gamma1,1.
On a class of non-simply connected Calabi-Yau threefolds
2007
We obtain a detailed classification for a class of non-simply connected Calabi-Yau threefolds which are of potential interest for a wide range of problems in string phenomenology. These threefolds arise as quotients of Schoen's Calabi-Yau threefolds, which are fiber products over P1 of two rational elliptic surfaces. The quotient is by a freely acting finite abelian group preserving the fibrations. Our work involves a classification of restricted finite automorphism groups of rational elliptic surfaces.