Codimension-3 Singularities and Yukawa Couplings in F-theory

By Hirotaka Hayashi, T. Kawano, R. Tǎtar, T. Watari. 2009

197 citations recorded by the source corpus.

Abstract F-theory is one of the frameworks where all the Yukawa couplings of grand unified theories are generated and their computation is possible. The Yukawa couplings of charged matter multiplets are supposed to be generated around codimension-3 singularity points of a base complex 3-fold, and that has been confirmed for the simplest type of codimension-3 singularities in recent studies. However, the geometry of F-theory compactifications is much more complicated. For a generic F-theory compactification, such issues as flux configuration around the codimension-3 singularities, field-theory formulation of the local geometry and behavior of zero-mode wavefunctions have virtually never been addressed before. We address all these issues in this article, and further discuss nature of Yukawa couplings generated at such singularities. In order to calculate the Yukawa couplings of low-energy effective theory, however, the local descriptions of wavefunctions on complex surfaces and a global characterization of zero-modes over a complex curve have to be combined together. We found the relation between them by re-examining how chiral charged matters are characterized in F-theory compactification. An intrinsic definition of spectral surfaces in F-theory turns out to be the key concept. As a biproduct, we found a new way to understand the Heterotic–F theory duality, which improves the precision of existing duality map associated with codimension-3 singularities.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/653e71e130da40f3619e67698794b5023cc03d19

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Citations in the corpus

F-theory fluxes, chirality and Chern-Simons theories (2011, background): “These assumptions are exploited already in [27, 3, 4, 28] and have been studied for compact settings in [13, 18].”
G(4)-flux, chiral matter and singularity resolution in F-theory compactifications (2011, background): “However, since we are interested here in models with U(1)X symmetry the analogous spectral cover is of the socalled split type [28], [29],[16], generalising the construction of S[U(N)×U(1)] spectral cover bundles from the heterotic string [54–56].”
Anomaly equations and intersection theory (2011, background): “Acknowledgement First and foremost I would like to thank Wati Taylor for his guidance, support and en(12)An incomplete list of references on the structure of four-dimensional F-theory backgrounds is given in the bibliography [25, 52, 55, 58, 79, 80, 81, 82, 83, 84].”
Higgs Bundles and UV Completion in F-Theory (2009, methodology): “we have to tune the complex structure (1)This observation was made independently in [10], which appeared while this project was written up.”
Global F-theory GUTs (2009, background): “In [26, 27] it was realized that a natural description of certain geometric aspects and the gauge flux is in terms of the spectral cover construction, which first came to stage in string theory in the context of heterotic compactifications [28, 29].”
Small resolutions of SU(5)-models in F-theory (2011, background): “13) The curve Σ5 contains additional points Π7 : w = P = R = 0 over which the singular fiber I6 is conjectured to enhance further to a fiber of type I7 [24, 31]: Π7 : w = P = R = 0 (I7?).”
Lectures on F-theory compactifications and model building (2010, background): “As found in [61], however, typically Pm and PH intersect at points without further singularity enhancements.”
T-branes and monodromy (2010, methodology): “For example, in [12] it was postulated that the localized matter content of a monodromic background was specified by a diagonal Higgs field with branch cuts.”
MODELS OF PARTICLE PHYSICS FROM TYPE IIB STRING THEORY AND F-THEORY: A REVIEW (2012, background): “1, the SU(5)⊥ singularity has a Weyl group action which interchanges the ti so as to preserve the bi and generally the fibration over SGUT can act with this group which gives rise to monodromies in F-theory [227,235,246].”
G-flux in F-theory and algebraic cycles (2011, methodology): “Following [62, 63], the powerful technique of the spectral cover was introduced in [5, 7] to describe the gauge flux in F-theory, and to compute the number of chiral modes generated by this flux on the matter curves.”
U(1) symmetries in F-theory GUTs with multiple sections (2012, background): “Generally the fibration over SGUT can act with this group which in F-theory is termed monodromies [31, 12].”
New aspects of Heterotic–F-theory duality (2008, background): “14 Note added in version 4: it is now understood clearly [52] why the type (a) and type (b) points do not contribute to the divisor of the line bundle (77).”