-flux, chiral matter and singularity resolution in F-theory compactifications

Abstract

Abstract:We construct a set of chirality inducing G 4 -fluxes in global F-theory compactifications on Calabi-Yau four-folds. Special emphasis is put on models with gauge group SU (5) × U (1) X relevant in the context of F-theory GUT model building, which are described in terms of a U (1)-restricted Tate model. A G 4 -flux arises in a manner completely analogous to the U (1) X gauge potential. We describe in detail the resolution by blow-up of the various singularities responsible for the U (1) X factor and the standard SU (5) gauge group and match the result with techniques applied in the context of toric geometry. This provides an explicit identification of the structure of the resolved fibre over the matter curves and over the enhancement points relevant for Yukawa couplings. We compute the flux-induced chiral index both of SU (5) charged matter and of SU (5) singlets charged only under U (1) X localised on curves which are not contained in the SU (5) locus. We furthermore discuss global consistency conditions such as D3-tadpole cancellation, D-term supersymmetry and Freed-Witten quantisation. The U (1) X gauge flux is a global extension of a class of split spectral cover bundles. It constitutes an essential ingredient in the construction of globally defined F-theory compactifications with chiral matter. We exemplify this in a three-generation SU (5) × U (1) X model whose flux satisfies all of the above global consistency conditions. We also extend our results to chiral fluxes in models without U (1) restriction.arXiv:1109.3454v2 [hep-th]

The Tate form on steroids: resolution and higher codimension fibers

“…Likewise, along b 1 = b 3 = 0 the fibers are Kodaira D type with the correct multiplicities, which appears to be different from the findings in [8], however, is in agreement with all the multiplicities obtained in [9]. Note that later on in the context of SU(5) × U(1) models [27], the multiplicities in [9] were also confirmed. There is an interesting network of small resolutions which gives rise to different splittings of the matter curves and will be discussed elsewhere [38].…”

“…The geometry obtained after proper transformation, corresponding to a Calabi-Yau with a resolved SO(4k + 4) singularity, is then 27) along with the projectivity conditions between the sections given in appendix C.3.…”

“…In particular G-flux G 4 ∈ H 2,2 (Y, Z) can be constructed in terms of surfaces in the resolved geometry, and proper quantization can be checked using the c 2 of the resolved fourfold [9,17,21,[26][27][28][29]. Likewise for general gauge groups, the resolved geometries in this paper can be applied to construct such G-flux.…”

“…with additional U(1) factors and connection to orientifold limits, the resolved geometries were studied in [27,29,[32][33][34][35][36][37]. The outline of the paper is as follows.…”

Six-dimensional origin of N $$ \mathcal{N} $$ = 4 SYM with duality defects

“…From the point of view of the 2d chiral theories, this corresponds to loci of enhanced flavor symmetries, which can be determined by studying the mechanics of the singular fibers which have an enhanced singularity above these points [10][11][12][13][14][15].…”