1. Constraints on standard model constructions in F-theoryMirjam Cvetič, James Halverson, Ling Lin, Cody Long, 2020, izvirni znanstveni članek Opis: 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. Ključne besede: brane worlds, compactification, string theory Objavljeno v DKUM: 23.10.2023; Ogledov: 380; Prenosov: 11 Celotno besedilo (292,32 KB) Gradivo ima več datotek! Več... |
2. Statistics of limit root bundles relevant for exact matter spectra of F-theory MSSMsMartin Bies, Mirjam Cvetič, Mingqiang Liu, 2021, izvirni znanstveni članek Opis: 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. Ključne besede: astrophysics, compactification, string theory models, geometry, higher-dimensional field theories, mathematical physics, quantum fields in curved spacetime, string phenomenology, supersymmetric models, topology Objavljeno v DKUM: 16.10.2023; Ogledov: 218; Prenosov: 11 Celotno besedilo (444,13 KB) Gradivo ima več datotek! Več... |
3. Gauge group topology of 8D Chaudhuri-Hockney-Lykken vacuaMirjam Cvetič, Markus Dierigl, Ling Lin, Hao Y. Zhang, 2021, izvirni znanstveni članek Opis: Compactifications of the Chaudhuri-Hockney-Lykken (CHL) string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice ΛM, the so-called Mikhailov lattice. Based on these data, we devise a method to determine the global gauge group structure including all Uð1Þ factors. The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual. Interpreting a nontrivial π1ðGÞ ≡ Z for the non-Abelian gauge group G as having gauged a Z 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly [1] that would obstruct this gauging. We verify this by explicitly computing Z for all 8D CHL vacua with rankðGÞ ¼ 10. Since our method applies also to T2 compactifications of heterotic strings, we further establish a map that determines any CHL gauge group topology from that of a “parent” heterotic model. Ključne besede: astrophysics, compactification, string dualities, string and branes, discrete symmetries, symmetries, gauge symmetries Objavljeno v DKUM: 13.10.2023; Ogledov: 343; Prenosov: 14 Celotno besedilo (356,95 KB) Gradivo ima več datotek! Več... |
4. Higher-form symmetries and their anomalies in M-/F-theory dualityMirjam Cvetič, Markus Dierigl, Ling Lin, Hao Y. Zhang, 2021, izvirni znanstveni članek Opis: We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations of the gauge group topology in F-theory via Mordell-Weil torsion and string junctions. We further study dimensional reductions of the 11d Chern-Simons term in the presence of torsional boundary G4-fluxes, which encode background gauge fields of center one-form symmetries in the lower-dimensional effective gauge theory. We find contributions that can be interpreted as ’t Hooft anomalies involving the one-form symmetry which originate from a fractionalization of the instanton number of non-Abelian gauge theories in F-/M-theory compactifications to 8d=7d and 6d=5d. Ključne besede: astrophysics, anomalies, compactification, M-theory, string dualities, discrete symmetries, symmetries Objavljeno v DKUM: 13.10.2023; Ogledov: 340; Prenosov: 4 Celotno besedilo (752,29 KB) Gradivo ima več datotek! Več... |
5. Reflections on the matter of 3D N=1 vacua and local Spin(7) compactificationsMirjam Cvetič, Jonathan J. Heckman, Ethan Torres, Gianluca Zoccarato, 2022, izvirni znanstveni članek Opis: We use Higgs bundles to study the 3D N = 1 vacua obtained from M-theory compactified on a local Spin(7) space given as a four-manifold M-4 of ADE singularities with further generic enhancements in the singularity type along one-dimensional subspaces. There can be strong quantum corrections to the massless degrees of freedom in the low energy effective field theory, but topologically robust quantities such as "parity" anomalies are still calculable. We show how geometric reflections of the compactification space descend to 3D reflections and discrete symmetries. The parity anomalies of the effective field theory descend from topological data of the compactification. The geometric perspective also allows us to track various perturbative and nonperturbative corrections to the 3D effective field theory. We also provide some explicit constructions of well-known 3D theories, including those which arise as edge modes of 4D topological insulators, and 3D N = 1 analogs of grand unified theories. An additional result of our analysis is that we are able to track the spectrum of extended objects and their transformations under higher-form symmetries. Ključne besede: Compactification, geometry, M-theory, quantum field theory, string theory techniques in condensed matter, strings & branes, supersymmetry, topology Objavljeno v DKUM: 25.09.2023; Ogledov: 213; Prenosov: 18 Celotno besedilo (910,15 KB) Gradivo ima več datotek! Več... |
6. Qualitative Studies of Some Polynomial Systems of Ordinary Differential EquationsMaša Dukarić, 2016, doktorska disertacija Opis: This doctoral dissertation is devoted to the studies of some qualitative properties of certain polynomial systems of ordinary differential equations. The main problems that are considered in this thesis are the problems of integrability and cyclicity. Some results on the classification of the global phase portraits of a family of cubic systems are presented as well. In the first chapter basic notions and results of the qualitative theory of systems of ODE's are introduced. Since one of important tools for our study of these problems is the commutative computational algebra, some main notions and properties of polynomial ideals and their varieties, including various algorithms related to them, are also presented in the introduction. In the second chapter methods for investigation of trajectories near degenerated singularities are presented. They are further used for the classification of global phase portraits of a family of cubic systems with the nilpotent center at the origin. In the third chapter the main problem of these thesis is studied, the problem of integrability. The problem of integrability which is connected to the problem of distinguishing between a center and a focus is studied for two different families of cubic polynomial systems of ODE's. With the computational algebra approach the necessary conditions for the existence of the first integral of these systems were obtained. For all but one condition was proven, using various approaches, the existence of the first integrals. The center problem for the real systems can be generalized to the complex systems. The origin of the system obtained after the complexification of the real system is the so-called 1:-1 resonant singular point, from which one additional generalization follows. This is the generalization to the p:-q resonant center. In the third chapter the :-3 resonant singular point of a quadratic family of complex systems is studied. The fourth chapter is devoted to the study of the problem of integrability of a three dimensional polynomial system with quadratic nonlinearities. The problem of existence of two independent first integrals and the existence of one first integral in the system was investigated. In the last chapter local bifurcations of limit cycles of a family of cubic systems are studied. Estimations for the number of limit cycles bifurcated from each components of the center variety are obtained. Ključne besede: planar systems of ODE's, higher dimensional systems of ODE's, phase portrait, nilpotent center, limit cylces, Poincaré compactification, center problem, Bautin ideal, focus quantities, time-reversibility, integrability problem, Darboux method, linearizability, limit cycle, cyclicity Objavljeno v DKUM: 19.07.2016; Ogledov: 2024; Prenosov: 280 Celotno besedilo (12,26 MB) |
7. Two constructions of continua: inverse limits and compactificationsTina Sovič, 2013, doktorska disertacija Opis: In the thesis we talk about two different constructions of continua. First we present the generalized inverse limits, with help of which we construct Wazewski's universal dendrite. What follows is a description of the compactifications of a ray and the presentation of results about their span.
The first chapter will be an introduction to the continuum theory trough interesting examples, as sin(1/x)-continuum, Hilbert cube, Brouwer-Janiszewski-Knaster continuum and pseudoarc. We will present some of their properties, among which irreducibility, smoothness and span zero are the most important ones for us.
In the continuation we intend to present some various constructions of continua. The main focus will be on the generalized inverse limits and compactifications of rays, which will also be a central part of the thesis. In this chapter, we also study inverse limits in the category of compact Hausdorff spaces with upper semi-continuous functions. We show that the inverse limits with upper semi-continuous bonding functions, together with the projections are weak inverse limits in this category.
The following two are the most important chapters in the thesis. The first is a detailed description of a construction of the family of upper semi-continuous functions f, such that the inverse limit of the inverse sequence of unit intervals and f, as the only bonding function, is homeomorphic to Wazewski's universal dendrite for each of it. Among other results we will also give a complete characterization of comb-functions, for which the inverse limits of the type described above are dendrites.
The next important chapter will be about compactifications of rays. In the first part of this chapter we will use compactifications to prove that for each continuum Y there is an irreducible smooth continuum that contains a topological copy of Y. The second part presents the main results of this chapter; i.e. the span of a compactification of a ray with a remainder that has a span zero is also zero. In the proofs of this chapter we will help ourselves with a discretization of span. Ključne besede: continua, inverse limit, inverse sequence, upper semi-continuous function, set-valued functions, bonding function, hyperspace, dendrite, universal dendrite, category, compactification, compactification of a ray, smooth continua, irreducible continua, span, span zero Objavljeno v DKUM: 25.09.2013; Ogledov: 2156; Prenosov: 169 Celotno besedilo (861,84 KB) |