Abelian gauge symmetries and proton decay in global F-theory GUTs

By Thomas W. Grimm, T. Weigand. 2010

241 citations recorded by the source corpus.

The existence of Abelian gauge symmetries in four-dimensional $F$-theory compactifications depends on the global geometry of the internal Calabi-Yau four-fold and has important phenomenological consequences. We study conceptual and phenomenological aspects of such $U(1)$ symmetries along the Coulomb and the Higgs branch. As one application we examine Abelian gauge factors arising after a certain global restriction of the Tate model that goes beyond a local spectral cover analysis. In $SU(5)$ grand unified theory (GUT) models this mechanism enforces a global $U(1{)}_{X}$ symmetry that prevents dimension-4 proton decay and allows for an identification of candidate right-handed neutrinos. We invoke a detailed account of the singularities of Calabi-Yau four-folds and their mirror duals starting from an underlying ${E}_{8}$ and ${E}_{7}\ifmmode\times\else\texttimes\fi{}U(1)$ enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyze $F$-theory GUT models.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/25bd1856b301b0f31ea43ea8a51df82b11babeff

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Citations in the corpus

Anomaly cancellation and abelian gauge symmetries in F-theory (2012, methodology): “ll construct the singular fourfold leading to SU(5) U(1) gauge symmetry by starting with a singular fourfold with only an SU(5) singularity. Then we apply the method of the U(1)-restricted Tate model [25] to generate a new section of the elliptic bration of the fourfold. This means that the complex ”
G(4)-flux, chiral matter and singularity resolution in F-theory compactifications (2011, methodology): “n one. This gives rise to an exceptional divisor fs= 0g. Its dual two-form leads to an extra U(1) gauge potential upon expanding the M-theory three-form C 3 as C 3 = A^w X with w X = [S]+[Z]+c 1(B 3) [27].3 Obviously, this construction provides a natural candidate for the U(1) X ux G 4 = F^w X [32].”
F-theory on all toric hypersurface fibrations and its Higgs branches (2014, background): “The divisor classes that support Abelian gauge fields in F-theory [34,39,77], see also [22,31,78], are obtained from the Shioda map σ of the rational sections ŝm.”
F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds (2012, background): “. – 30 – Variety M N P(1,2,3) z6 x3 y2 ✁ ✁ ✁ ✁ ❅✁ ❅ ❅ ❅ ❅ t t t t t t ❞ Dz Dx Dy ✁ ✁ ✁ ✁ ❅✁ ❅ ❅ ❅ ❅ t t t t t t ❞ P(1,1,2) u4 v4 w2 ❅t ❅ ❅ ❅ ❅ t t t t t t t ❞ Du Dv Dw ✁ ✁ ✁ ✁ ❆✁ ❆ ❆ ❆ ❆ t t t t ❞ Bl [0,1,0]P (1,1,2) u4 uv3 v2w w2 ❅t ❅ ❅ ❅ ❅ t t t t t t ❞ Du Dv Dw E 1 ✁ ✁ ✁ ✁ ❅✁ ❅❅ t t t t t ❞ Z u3v”
Lectures on F-theory compactifications and model building (2010, methodology): “These localized states appear at self-intersections of the I1-part S1 of the discriminant, along which the gauge group enhances to A1 [37].”
The Swampland: Introduction and Review (2019, background): “simple example of a general relation in string theory between geometry, gauge fields and charged states, which has been studied in great detail, see [277–286] for example.”
Anomaly equations and intersection theory (2011, background): “(6)Determining the abelian gauge symmetry is subtle in a wide variety of string constructions, including heterotic, orbifold, intersecting brane, fractional brane and F-theory models [3, 8, 9, 32, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55].”
Geometric engineering in toric F-theory and GUTs with U(1) gauge factors (2013, background): “Studying global U(1) symmetries is a topic of intense current research [11, 12, 13, 14, 15, 16, 17, 18, 19].”
U(1) symmetries in F-theory GUTs with multiple sections (2012, background): “ investigations of U(1) symmetries in six-dimensional F-theory compactications 3 have appeared early on in [27]. In the context of SU(5) GUTs one approach to realising massless U(1)s was proposed in [4] in terms of what was called an U(1)-restricted Tate model. The idea was to choose the coecients o”
F-theory fluxes, chirality and Chern-Simons theories (2011, methodology): “The geometric construction presented here corresponds to the U(1) restricted Tate model introduced in [8].”
G-flux in F-theory and algebraic cycles (2011, methodology): “ngularities, which we will do in section 4.2.1. The result diﬀers from the geometric tadpole of the smooth fourfold we have started with. In the present situation, the diﬀerence is given by (see also [67]): 9 Z B3 K¯3. (4.29) As the tadpole has to be cancelled both before and after the transition, t”
MODELS OF PARTICLE PHYSICS FROM TYPE IIB STRING THEORY AND F-THEORY: A REVIEW (2012, background): “ case where z 1 = 1 we have that P T(x 1;y 1;1) = 0 and therefore if we transform coordinates by x!x+ x 1 and y!y+ y 1 we arrive at a form for P T where a 6 = 0. This is the case which was studied in [189], termed a U(1)-restricted Tate Model, where it was shown that the additional section generical”
F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections (2013, background): “This additional structure has rich phenomenological implications in Beyond the Standard Model (BSM) model building, where it can be used to avoid dangerous proton decay operators, engineer realistic Yukawa textures or provide a solution to the μ-problem [6, 27, 47, 39, 48, 30].”