New aspects of Heterotic–F-theory duality

By Hirotaka Hayashi, R. Tǎtar, Yukinobu Toda, T. Watari, Masahito Yamazaki. 2008

189 citations recorded by the source corpus.

Abstract In order to understand both up-type and down-type Yukawa couplings, F-theory is a better framework than the perturbative Type IIB string theory. The duality between the Heterotic and F-theory is a powerful tool in gaining more insights into F-theory description of low-energy chiral multiplets. Because chiral multiplets from bundles ∧ 2 V and ∧ 2 V × as well as those from a bundle V are all involved in Yukawa couplings in Heterotic compactification, we need to translate descriptions of all those kinds of matter multiplets into F-theory language through the duality. We find that chiral matter multiplets in F-theory are global holomorphic sections of line bundles on what we call covering matter curves. The covering matter curves are formulated in Heterotic theory in association with normalization of spectral surface, while they are where M2-branes wrapped on a vanishing two-cycle propagate in F-theory. Chirality formulae are given purely in terms of primitive four-form flux. In order to complete the translation, the dictionary of the Heterotic–F-theory duality has to be refined in some aspects. A precise map of spectral surface and complex structure moduli is obtained, and with the map, we find that divisors specifying the line bundles correspond precisely to codimension-3 singularities in F-theory.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/98085c3757eb12cff478b79df292d3684bb3c03c

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Citations in the corpus

F-theory Compactifications for Supersymmetric GUTs (2009, background): “Some aspects of the heterotic/F-theory duality map that helped elucidate important structures in F-theory have been discussed recently in [11, 26].”
F-theory fluxes, chirality and Chern-Simons theories (2011, methodology): “A first approach in the derivation of a chirality formula for the charged matter fields along the intersection of two 7-branes was to use the local data of the geometry and gauge bundle [3, 4, 5].”
G-flux in F-theory and algebraic cycles (2011, methodology): “It hence seems natural that the chirality can be obtained as the integral of G4 over these curves [3, 6].”
GUTs in Type IIB Orientifold Compactifications (2008, background): “The local model building rules for such F-theory compactifications have been worked out recently in [13,14,15,16,17,18,19]; For recent studies of 7-branes from the F-theory perspective see [20, 21, 22, 23, 24].”
Global F-theory GUTs (2009, background): “For simplicity we will not introduce this spectral cover explicitly here, but note that, unlike C((5)), it is singular along a curve of double point singularities [1, 50].”
Torsional Heterotic Geometries (2009, unknown): “1kbecker@physics.tamu.edu 2sethi@uchicago.edu”
Higgs Bundles and UV Completion in F-Theory (2009, methodology): “This recovers the answer found in [3].”
F-theory GUT vacua on compact Calabi-Yau fourfolds (2009, methodology): “21) The computation of the matter curve for 5m and 5H is much more complicated due to singularities in the associated antisymmetrised spectral cover [59, 60, 38, 15].”
G(4)-flux, chiral matter and singularity resolution in F-theory compactifications (2011, background): “From general arguments [2, 6], this flux leads to a chiral index for matter states charged under U(1)X by integration of G4 over the associated matter surfaces.”
F-theory on all toric hypersurface fibrations and its Higgs branches (2014, background): “String backgrounds constructed via F-theory are not only located in the heart of the web of string dualities, but also allow for the construction of phenomenologically appealing local GUT-models [4–7], which has recently rekindled a lot of interest into the subject.”
Monodromies, Fluxes, and Compact Three-Generation F-theory GUTs (2009, methodology): “To obtain a prescription for picking out the 5 matter curve inside C10, we follow the heterotic literature (see for instance [19, 20, 21]) and define an involution τ : X → X by sending V → −V , which inverts the sheets of C10 according to λi → −λi.”
Codimension-3 Singularities and Yukawa Couplings in F-theory (2009, methodology): “The behavior of the zero-mode wavefunctions are determined by using the 8-dimensional field-theory formulation of [4, 5], and we find that the results agree with what was obtained in [6] by using Heterotic–F theory duality.”
Breaking GUT groups in $F$-theory (2008, methodology): “(5)More precisely, if the matter curve is singular (as is the case for Σ 5 ) it turns out that chiral matter naturally propagates on a smooth covering of the curve (namely the normalization), and one obtains line bundles on the smooth covers of the matter curves [14].”
Compact F-theory GUTs with U(1)PQ (2009, methodology): “This analysis was inspired by studies of matter curves in models with heterotic duals [29, 30, 31].”