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Generalized cut method for computing Szeged-like polynomials with applications to polyphenyls and carbon nanocones
Simon Brezovnik, Niko Tratnik, 2023, original scientific article

Abstract: Szeged, Padmakar-Ivan (PI), and Mostar indices are some of the most investigated distance-based Szeged-like topological indices. On the other hand, the polynomials related to these topological indices were also introduced, for example the Szeged polynomial, the edge- Szeged polynomial, the PI polynomial, the Mostar polynomial, etc. In this paper, we introduce a concept of the general Szeged-like polynomial for a connected strength-weighted graph. It turns out that this concept includes all the above mentioned polynomials and also infinitely many other graph polynomials. As the main result of the paper, we prove a cut method which enables us to efficiently calculate a Szeged-like polynomial by using the corresponding polynomials of strength-weighted quotient graphs obtained by a partition of the edge set that is coarser than ▫$\Theta^*$▫-partition. To the best of our knowledge, this represents the first implementation of the famous cut method to graph polynomials. Finally, we show how the deduced cut method can be applied to calculate some Szeged-like polynomials and corresponding topological indices of para-polyphenyl chains and carbon nanocones.
Keywords: graph theory, carbon nanocone, topological indices
Published in DKUM: 25.03.2024; Views: 74; Downloads: 1
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Home gardening and food security concerns during the COVID-19 pandemic
Maja Turnšek, S. L. Gangenes Skar, Marit Piirman, Ragnheidur Thorarinsdottir, Martina Bavec, Ranka Junge-Berberovic, 2022, original scientific article

Abstract: At times of crisis, home gardening has often been sought out as a potential solution for threats to food security and as a measure to increase socio-psychological effects, such as public sense of self-efficacy, trust in the government and care for one’s wellbeing. The objective of this study was to investigate if home gardening increased during the COVID-19 pandemic in the spring/summer of 2020 and to provide socio-psychological insights into the explanatory factors of such an increase. An explanatory theoretical model of home gardening was proposed and tested to analyse whether home gardening is correlated to food security concerns, and if so, to what extent. A nonrepresentative survey was conducted in five European countries (Slovenia, Norway, Estonia, Switzerland, and Iceland) using snowball sampling via social media networks, reaching 1144 participants. The results showed the pandemic did prove to be an important psychological push towards home gardening prompted by food security concerns. Measured as loose as introducing at least one new gardening activity during COVID-19, this study found an approximately 10% increase in home gardening during the first wave of COVID-19 in the sample population, which was skewed towards educated, female, middle-class Europeans.
Keywords: food security, home gardening, COVID-19, food security concerns, wellbeing, behavioural change, protection motivation theory
Published in DKUM: 16.01.2024; Views: 124; Downloads: 7
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Quadrillion F-theory compactifications with the exact chiral spectrum of the standard model
Mirjam Cvetič, James Halverson, Ling Lin, Mingqiang Liu, Jianjun Paul Tian, 2019, original scientific article

Abstract: We present O(10(15)) string compactifications with the exact chiral spectrum of the standard model of particle physics. This ensemble of globally consistent F-theory compactifications automatically realizes gauge coupling unification. Utilizing the power of algebraic geometry, all global consistency conditions can be reduced to a single criterion on the base of the underlying elliptically fibered Calabi-Yau fourfolds. For toric bases, this criterion only depends on an associated polytope and is satisfied for at least O(10(15)) bases, each of which defines a distinct compactification.
Keywords: FLUX, F-theory, string compactifications, chiral spectrum
Published in DKUM: 23.10.2023; Views: 357; Downloads: 11
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Constraints on standard model constructions in F-theory
Mirjam Cvetič, James Halverson, Ling Lin, Cody Long, 2020, original scientific article

Abstract: We argue that the following three statements cannot all be true: (i) our vacuum is a type IIB/F-theory vacuum at moderate to large h(1,1); (ii) the alpha' expansion is controlled via the supergravity approximation, a la the Kachru-Kallosh-Linde-Trivedi and Large Volume scenarios; and (iii) there are no additional gauged sectors from 7-branes. Since nearly all known globally consistent F-theory models with the exact chiral spectrum of the Standard Model and gauge coupling unification occur at moderate h(1,1), this finding calls for new moduli stabilization scenarios or/and a rich 7-brane dark sector.
Keywords: brane worlds, compactification, string theory
Published in DKUM: 23.10.2023; Views: 337; Downloads: 11
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Geometric unification of Higgs bundle vacua
Mirjam Cvetič, Jonathan J. Heckman, Thomas B. Rochais, Ethan Torres, Gianluca Zoccarato, 2020, original scientific article

Abstract: Higgs bundles are a central tool used to study a range of intersecting brane systems in string compactifications. Solutions to the internal gauge theory equations of motion for the corresponding worldvolume theories of brans give rise to different low energy effective field theories. This has been heavily used in the study of M-theory on local G(2) spaces and F-theory on local elliptically fibered CalabiYau fourfolds. In this paper we show that the 3D N = 1 effective field theory defined by M-theory on a local spin(7) space unifies the Higgs bundle data associated with 4D N = 1 M- and F-theory vacua. This 3D system appears as an interface with finite thickness between different 4D vacua. We develop the general formalism of M-theory on such local spin(7) spaces and build explicit interpolating solutions. This provides a complementary local gauge theory analysis of a recently proposed approach to constructing spin(7) spaces from generalized connected sums.
Keywords: F-theory, Higgs, M-theory, field theories, spin spices
Published in DKUM: 23.10.2023; Views: 317; Downloads: 11
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String Universality and Non-Simply-Connected Gauge Groups in 8D
Mirjam Cvetič, Markus Dierigl, Ling Lin, Hao Y. Zhang, 2020, original scientific article

Abstract: We present a consistency condition for 8D N 1 supergravity theories with nontrivial global structure G=Z for the non-Abelian gauge group, based on an anomaly involving the Z 1-form center symmetry. The interplay with other swampland criteria identifies the majority of 8D theories with gauge group G=Z, which have no string theory realization, as inconsistent quantum theories when coupled to gravity. While this condition is equivalent to geometric properties of elliptic K3 surfaces in F-theory compactifications, it constrains the unexplored landscape of gauge groups in other 8D string models.
Keywords: supergravity theories, string theory, 8D string models
Published in DKUM: 16.10.2023; Views: 389; Downloads: 15
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Yukawa hierarchies in global F-theory models
Mirjam Cvetič, Ling Lin, Mingqiang Liu, Hao Y. Zhang, Gianluca Zoccarato, 2020, original scientific article

Abstract: We argue that global F-theory compactifications to four dimensions gener- ally exhibit higher rank Yukawa matrices from multiple geometric contributions known as Yukawa points. The holomorphic couplings furthermore have large hierarchies for generic complex structure moduli. Unlike local considerations, the compact setup realizes these features all through geometry, and requires no instanton corrections. As an example, we consider a concrete toy model with SU(5) x U(1) gauge symmetry. From the geometry, we find two Yukawa points for the 10-25-4 coupling, producing a rank two Yukawa matrix. Our methods allow us to track all complex structure dependencies of the holomorphic couplings and study the ratio numerically. This reveals hierarchies of O(10(5)) and larger on a full-dimensional subspace of the moduli space.
Keywords: F-theory, supersymmetric effective theories
Published in DKUM: 16.10.2023; Views: 132; Downloads: 11
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Conformal symmetries for extremal black holes with general asymptotic scalars in STU supergravity
Mirjam Cvetič, Christopher N. Pope, Aritra Saha, 2021, original scientific article

Abstract: We present a construction of the most general BPS black holes of STU supergravity (N = 2 supersymmetric D = 4 supergravity coupled to three vector supermultiplets) with arbitrary asymptotic values of the scalar fields. These solutions are obtained by acting with a subset of the global symmetry generators on STU BPS black holes with zero values of the asymptotic scalars, both in the U-duality and the heterotic frame. The solutions are parameterized by fourteen parameters: four electric and four magnetic charges, and the asymptotic values of the six scalar fields. We also present BPS black hole solutions of a consistently truncated STU supergravity, which are parameterized by two electric and two magnetic charges and two scalar fields. These latter solutions are significantly simplified, and are very suitable for further explicit studies. We also explore a conformal inversion symmetry of the Couch-Torrence type, which maps any member of the fourteen-parameter family of BPS black holes to another member of the family. Furthermore, these solutions are expected to be valuable in the studies of various swampland conjectures in the moduli space of string compactifications.
Keywords: black holes, extended supersymmetry, supergravity models, string theory
Published in DKUM: 16.10.2023; Views: 205; Downloads: 12
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Root bundles and towards exact matter spectra of F-theory MSSMs
Martin Bies, Mirjam Cvetič, Ron Donagi, Mingqiang Liu, Marielle Ong, 2021, original scientific article

Abstract: Motivated by the appearance of fractional powers of line bundles in studies of vector-like spectra in 4d F-theory compactifications, we analyze the structure and origin of these bundles. Fractional powers of line bundles are also known as root bundles and can be thought of as generalizations of spin bundles. We explain how these root bundles are linked to inequivalent F-theory gauge potentials of a G(4)-flux. While this observation is interesting in its own right, it is particularly valuable for F-theory Standard Model constructions. In aiming for MSSMs, it is desired to argue for the absence of vector-like exotics. We work out the root bundle constraints on all matter curves in the largest class of currently-known F-theory Standard Model constructions without chiral exotics and gauge coupling unification. On each matter curve, we conduct a systematic "bottom"-analysis of all solutions to the root bundle constraints and all spin bundles. Thereby, we derive a lower bound for the number of combinations of root bundles and spin bundles whose cohomologies satisfy the physical demand of absence of vector-like pairs. On a technical level, this systematic study is achieved by a well-known diagrammatic description of root bundles on nodal curves. We extend this description by a counting procedure, which determines the cohomologies of so-called limit root bundles on full blow-ups of nodal curves. By use of deformation theory, these results constrain the vector-like spectra on the smooth matter curves in the actual F-theory geometry.
Keywords: F-theory, differential geometry, algebraic geometry
Published in DKUM: 16.10.2023; Views: 200; Downloads: 15
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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: 172; Downloads: 11
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