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2. General lower bounds for the minor crossing number of graphsDrago Bokal, Éva Czabarka, László Székely, Imrich Vrt'o, 2008 Opis: There are three general lower bound techniques for the crossing numbers of graphs: the Crossing Lemma, the bisection method and the embedding method. Inthis contribution, we present their adaptations to the minor crossing number. Using the adapted bounds, we improve on the known bounds on the minor crossing number of hypercubes. We also point out relations of the minor crossing number to string graphs. Ključne besede: teorija grafov, prekrižno število, minor, hiper kocke, graph theory, minor crossing number, graph minor, string graphs, hypercubes Objavljeno: 10.07.2015; Ogledov: 335; Prenosov: 52 Povezava na celotno besedilo 
3. General lower bounds for the minor crossing number of graphsDrago Bokal, Éva Czabarka, László Székely, Imrich Vrt'o, 2010, izvirni znanstveni članek Opis: Obstajajo tri splošne spodnje meje za minorsko prekrižno število grafov: prekrižna lema, metoda z bisekcijo in metoda z vložitvami. V tem prispevku predstavimo njihove prilagoditve za minorsko prekrižno število grafov. S tako pridobljenimi spodnjimi mejami izboljšamo znane rezultate za minorsko prekrižno število hiperkock. Poleg navedenih rezultatov predstavimo tudi povezavo med minorskim prekrižnim številom in grafi, predstavljivimi s krivuljami (stringgraphs). Ključne besede: teorija grafov, minorsko prekrižno število, grafovski minor, krivuljski grafi, hiper kocke, graph theory, minor crossing number, graph minor, string graphs, hypercubes Objavljeno: 10.07.2015; Ogledov: 377; Prenosov: 70 Povezava na celotno besedilo 
4. SupergeometrodynamicsMirjam Cvetič, G. W. Gibbons, Christopher N. Pope, 2015, izvirni znanstveni članek Opis: We present explicit solutions of the timesymmetric initial value constraints, expressed in terms of freely specifiable harmonic functions for examples of supergravity theories, which emerge as effective theories of compactified string theory. These results are a prerequisite for the study of the timeevolution of topologically nontrivial initial data for supergravity theories, thus generalising the "Geometrodynamics" program of EinsteinMaxwell theory to that of supergravity theories. Specifically, we focus on examples of multiple electric Maxwell and scalar fields, and analyse the initial data problem for the general EinsteinMaxwellDilaton theory both with one and two Maxwell fields, and the STU model. The solutions are given in terms of up to eight arbitrary harmonic functions in the STU model. As a byproduct, in order compare our results with known static solutions, the metric in isotropic coordinates and all the sources of the nonextremal black holes are expressed entirely in terms of harmonic functions. We also comment on generalizations to timenonsymmetric initial data and their relation to cosmological solutions of gauged socalled fake supergravities with positive cosmological constant. Ključne besede: black holes, supergravity, string theory, conformal field models, string duality Objavljeno: 14.06.2017; Ogledov: 432; Prenosov: 59 Celotno besedilo (581,40 KB) Gradivo ima več datotek! Več...

5. Entanglement entropy of subtracted geometry black holesMirjam Cvetič, Zain H. Saleem, Alejandro Satz, 2015, polemika, diskusijski prispevek, komentar Opis: We compute the entanglement entropy of minimally coupled scalar fields on subtracted geometry black hole backgrounds, focusing on the logarithmic corrections. We notice that matching between the entanglement entropy of original black holes and their subtracted counterparts is only at the order of the area term. The logarithmic correction term is not only different but also, in general, changes sign in the subtracted case. We apply Harrison transformations to the original black holes and find out the choice of the Harrison parameters for which the logarithmic corrections vanish. Ključne besede: black holes, string theory Objavljeno: 14.06.2017; Ogledov: 367; Prenosov: 307 Celotno besedilo (378,41 KB) Gradivo ima več datotek! Več...

6. Black hole thermodynamics from a variational principle: asymptotically conical backgroundsSongok An, Mirjam Cvetič, Ioannis Papadimitriou, 2016, izvirni znanstveni članek Opis: The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for N = 2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called 'subtracted geometries'. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Surface terms play a crucial role in this identification. Ključne besede: MTheory, Black Holes, String Theory, Gaugegravity correspondence Objavljeno: 27.06.2017; Ogledov: 409; Prenosov: 241 Celotno besedilo (834,82 KB) Gradivo ima več datotek! Več...

7. Black holes with intrinsic spinMirjam Cvetič, Finn Larsen, 2014, izvirni znanstveni članek Opis: We analyze the general black hole solutions to the four dimensional STU model recently constructed by Chow and Compere. We define a dilute gas limit where the black holes can be interpreted as excited states of an extremal ground state. In this limit we express the black hole entropy and the excitation energy in terms of physical quantities with no need for parametric charges. We discuss a dual microscopic CFT description that incorporates all electric and magnetic charges. This description is recovered geometrically by identification of a near horizon BTZ region. We construct the subtracted geometry with no restrictions on charges by analyzing the scalar wave equation in the full geometry. We determine the matter sources that support the subtracted geometry by studying a scaling limit and show that the general geometry permits a dilute gas description with parameters that we specify. Ključne besede: black holes, string theory, conformal field models, string duality Objavljeno: 27.06.2017; Ogledov: 452; Prenosov: 231 Celotno besedilo (598,59 KB) Gradivo ima več datotek! Več...

8. Compactifications of deformed conifolds, branes and the geometry of qubitsMirjam Cvetič, G. W. Gibbons, Christopher N. Pope, 2016, izvirni znanstveni članek Opis: We present three families of exact, cohomogeneityone Einstein metrics in (2n + 2) dimensions, which are generalizations of the Stenzel construction of Ricciflat metrics to those with a positive cosmological constant. The first family of solutions are FubiniStudy metrics on the complex projective spaces CPn+1, written in a Stenzel form, whose principal orbits are the Stiefel manifolds V2(Rn+2) = SO(n+2)/SO(n) divided by Z(2). The second family are also EinsteinKahler metrics, now on the Grassmannian manifolds G(2)(Rn+3) = SO(n+3)/((SO(n+1)xSO(2)), whose principal orbits are the Stiefel manifolds V2(Rn+2) (with no Z(2) factoring in this case). The third family are Einstein metrics on the product manifolds Sn+1 x Sn+1, and are Kahler only for n = 1. Some of these metrics are believed to play a role in studies of consistent string theory compactifications and in the context of the AdS/CFT correspondence. We also elaborate on the geometric approach to quantum mechanics based on the Kahler geometry of FubiniStudy metrics on CPn+1, and we apply the formalism to study the quantum entanglement of qubits. Ključne besede: conformal field models, string theory, models of quantum gravity, differential geometry, algebraic geometry Objavljeno: 27.06.2017; Ogledov: 368; Prenosov: 246 Celotno besedilo (586,14 KB) Gradivo ima več datotek! Več...

9. Electrodynamics of black holes in STU supergravityMirjam Cvetič, G. W. Gibbons, Christopher N. Pope, Zain H. Saleem, 2014, izvirni znanstveni članek Opis: External magnetic fields can probe the composite structure of black holes in string theory. With this motivation we study magnetised fourcharge black holes in the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. We employ solution generating techniques to obtain Melvin backgrounds, and black holes in these backgrounds. For an initially electrically charged static black hole immersed in magnetic fields, we calculate the resultant angular momenta and analyse their global structure. Examples are given for which the ergoregion does not extend to infinity. We calculate magnetic moments and gyromagnetic ratios via Larmor's formula. Our results are consistent with earlier special cases. A scaling limit and associated subtracted geometry in a single surviving magnetic field is shown to lift to AdS(3) x S2. Magnetizing magnetically charged black holes give static solutions with conical singularities representing strings or struts holding the black holes against magnetic forces. In some cases it is possible to balance these magnetic forces. Ključne besede: black holes, supergravity, string theory, conformal field models, string duality Objavljeno: 27.06.2017; Ogledov: 391; Prenosov: 244 Celotno besedilo (563,26 KB) Gradivo ima več datotek! Več...

10. On finiteness of type IIB compactificationsMirjam Cvetič, James Halverson, Denis Klevers, Peng Song, 2014, izvirni znanstveni članek Opis: The string landscape satisfies interesting finiteness properties imposed by supersymmetry and stringtheoretical consistency conditions. We study N = 1 supersymmetric compactifications of Type IIB string theory on smooth elliptically fibered CalabiYau threefolds at large volume with magnetized D9branes and D5branes. We prove that supersymmetry and tadpole cancellation conditions imply that there is a finite number of such configurations. In particular, we derive an explicitly computable bound on the number of magnetic flux quanta, as well as the number of D5branes, which is independent of the continuous moduli of the setup. The proof applies if a number of easy to check geometric conditions of the twofold base are met. We show that these geometric conditions are satisfied for the almost Fano twofold bases given by each toric variety associated to a reflexive twodimensional polytope as well as by the generic del Pezzo surfaces dP(n) with n = 0, ..., 8. Physically, this finiteness proof shows that there exist a finite collection of fourdimensional gauge groups and chiral matter spectra in the 4D supergravity theories realized by these compactifications. As a byproduct we explicitly construct all generators of the Kaahler cones of dP(n) and work out their relation to representation theory. Ključne besede: black holes, supergravity, string theory, conformal field models, string duality Objavljeno: 27.06.2017; Ogledov: 421; Prenosov: 48 Celotno besedilo (1,01 MB) Gradivo ima več datotek! Več...
