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Statistics of limit root bundles relevant for exact matter spectra of F-theory MSSMs
Martin Bies, Mirjam Cvetič, Mingqiang Liu, 2021, original scientific article

Abstract: In the largest, currently known, class of one quadrillion globally consistent F-theory Standard Models with gauge coupling unification and no chiral exotics, the vectorlike spectra are counted by cohomologies of root bundles. In this work, we apply a previously proposed method to identify toric base threefolds, which are promising to establish F-theory Standard Models with exactly three quark doublets and no vectorlike exotics in this representation. The base spaces in question are obtained from triangulations of 708 polytopes. By studying root bundles on the quark-doublet curve Cð3;2Þ1=6 and employing well-known results about desingularizations of toric K3 surfaces, we derive a triangulation independent lower bound Nˇ ð3Þ P for the number Nð3Þ P of root bundles on Cð3;2Þ1=6 with exactly three sections. The ratio Nˇ ð3Þ P =NP, where NP is the total number of roots on Cð3;2Þ1=6 , is largest for base spaces associated with triangulations of the eighth three-dimensional polytope Δ∘ 8 in the Kreuzer-Skarke list. For each of these Oð1015Þ threefolds, we expect that many root bundles on Cð3;2Þ1=6 are induced from F-theory gauge potentials and that at least every 3000th root on Cð3;2Þ1=6 has exactly three global sections and thus no exotic vectorlike quark-doublet modes.
Keywords: astrophysics, compactification, string theory models, geometry, higher-dimensional field theories, mathematical physics, quantum fields in curved spacetime, string phenomenology, supersymmetric models, topology
Published in DKUM: 16.10.2023; Views: 219; Downloads: 11
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Machine learning and algebraic approaches towards complete matter spectra in 4d F-theory
Martin Bies, Mirjam Cvetič, Ron Donagi, Ling Lin, Mingqiang Liu, Fabian Ruehle, 2021, original scientific article

Abstract: Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d Ftheory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. To quantify jumps of these cohomologies, we first generate 1.8 million pairs of line bundles and curves embedded in dP3, for which we compute the cohomologies. A white-box machine learning approach trained on this data provides intuition for jumps due to curve splittings, which we use to construct additional vector-like Higgs-pairs in an F-Theory toy model. We also find that, in order to explain quantitatively the full dataset, further tools from algebraic geometry, in particular Brill-Noether theory, are required. Using these ingredients, we introduce a diagrammatic way to express cohomology jumps across the parameter space of each family of matter curves, which reflects a stratification of the F-theory complex structure moduli space in terms of the vector-like spectrum. Furthermore, these insights provide an algorithmically efficient way to estimate the possible cohomology dimensions across the entire parameter space.
Keywords: Differential Geometry, Algebraic Geometry, F-Theory, Flux Compactifications, Field Theories, Higher Dimensions
Published in DKUM: 13.10.2023; Views: 221; Downloads: 13
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Flavor symmetries and automatic enhancement in the 6D supergravity swampland
Mirjam Cvetič, Ling Lin, Andrew P. Turner, 2022, original scientific article

Abstract: We argue for the quantum-gravitational inconsistency of certain 6D N ¼ ð1; 0Þ supergravity theories, whose anomaly-free gauge algebra g and hypermultiplet spectrum M were observed by Raghuram et al. [J. High Energy Phys. 07 (2021) 048] to be realizable only as part of a larger gauge sector ðg0 ⊃ g; M0 ⊃ MÞ in F-theory. To detach any reference to a string theoretic method of construction, we utilize flavor symmetries to provide compelling reasons why the vast majority of such ðg; MÞ theories are not compatible with quantum gravity constraints, and how the “automatic enhancement” to ðg0 ; M0 Þ remedies this. In the first class of models, with g0 ¼ g ⊕ h, we show that there exists an unbroken flavor symmetry h acting on the matter M, which, if ungauged, would violate the no-global-symmetries hypothesis. This argument also applies to 1-form center symmetries, which govern the gauge group topology and massive states in representations different from those of massless states. In a second class, we find that g is incompatible with the flavor symmetry of certain supersymmetric strings that must exist by the completeness hypothesis.
Keywords: supergravity theories, supersymmetric strings, quantum gravity constraints, Gauge theories, Higher-dimensional field theories, strings & branes, supergravity, symmetries
Published in DKUM: 25.09.2023; Views: 180; Downloads: 7
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