Yukawas, G-flux, and spectral covers from resolved Calabi-Yau’s

By J. Marsano, Sakura Schafer-Nameki. 2011

181 citations recorded by the source corpus.

A bstractWe use the resolution procedure of Esole and Yau [1] to study Yukawa couplings, G-flux, and the emergence of spectral covers from elliptically fibered Calabi-Yau’s with a surface of A4 singularities. We provide a global description of the Esole-Yau resolution and use it to explicitly compute Chern classes of the resolved 4-fold, proving the conjecture of [2] for the Euler character in the process. We comment on the physical implications of the surprising singular fibers in codimension 2 and 3 in [1] and emphasize a group theoretic interpretation based on the A4 weight lattice. We then construct explicit G-fluxes by brute force in one of the 6 birationally equivalent Esole-Yau resolutions, quantize them explicitly using our result for the second Chern class, and compute the spectrum and flux-induced 3-brane charges, finding agreement with results and conjectures of local models in all cases. Finally, we provide a precise description of the spectral divisor formalism in this setting and sharpen the procedure described in [3] in order to explicitly demonstrate how the Higgs bundle spectral cover of the local model emerges from the resolved Calabi-Yau geometry. Along the way, we demonstrate explicitly how the quantization rules for fluxes in the local and global models are related.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5179c442ab72395f446a58d75604ac771cfdb2a1

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Citations in the corpus

Anomaly cancellation and abelian gauge symmetries in F-theory (2012, methodology): “We require the following integrals to vanish [12, 41], Θ0α = Θαβ = Θiα = 0 , (47)”
Anomaly equations and intersection theory (2011, background): “These contain information on the local matter we obtain [11, 12, 35, 36, 37, 38, 39, 40, 41].”
U(1) symmetries in F-theory GUTs with multiple sections (2012, methodology): “This resolution process has been studied with different techniques in the recent F-theory SU(5) GUT literature in a number of papers [22, 23, 24, 6, 7, 8] (see [25] for other gauge groups) and we use the process described in [6, 8].”
F-theory on all toric hypersurface fibrations and its Higgs branches (2014, methodology): “Finally, it would be interesting to use the toric hypersurface fibrations studied here also for compactifications of M-theory to engineer 3D N = 2 gauge theories and to study their Coulomb-branches and phase structures, see [106–109] (and also the seminal works [110, 111]) for recent detailed analys”
F-theory fluxes, chirality and Chern-Simons theories (2011, methodology): “The toric resolutions are equivalent, at least at co-dimension one and two relevant here, to the small resolutions performed for an SU(5) gauge group in [20, 13].”
G(4)-flux, chiral matter and singularity resolution in F-theory compactifications (2011, methodology): “A proposal for a global completion of spectral covers has been made in [53] and, for the case of non-split spectral covers, further subjected to global tests in [26].”
F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections (2013, background): “A recent reconsideration and careful analysis has closed remaining gaps in the understanding of singularities at higher codimension [19, 20, 21].”