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Compactifications of deformed conifolds, branes and the geometry of qubits
Mirjam Cvetič, G. W. Gibbons, Christopher N. Pope, 2016, izvirni znanstveni članek

Opis: We present three families of exact, cohomogeneity-one Einstein metrics in (2n + 2) dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of solutions are Fubini-Study metrics on the complex projective spaces CPn+1, written in a Stenzel form, whose principal orbits are the Stiefel manifolds V-2(Rn+2) = SO(n+2)/SO(n) divided by Z(2). The second family are also Einstein-Kahler 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 V-2(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 Fubini-Study 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: 42; Prenosov: 0
.pdf Polno besedilo (586,14 KB)

Chiral four-dimensional F-theory compactifications with SU(5) and multiple U(1)-factors
Mirjam Cvetič, Antonella Grassi, Denis Klevers, Hernan Piragua, 2014, izvirni znanstveni članek

Opis: We develop geometric techniques to determine the spectrum and the chiral indices of matter multiplets for four-dimensional F-theory compactifications on elliptic Calabi-Yau fourfolds with rank two Mordell-Weil group. The general elliptic fiber is the Calabi-Yau onefold in dP(2). We classify its resolved elliptic fibrations over a general base B. The study of singularities of these fibrations leads to explicit matter representations, that we determine both for U(1) xU(1) and SU(5) x U(1) x U(1) constructions. We determine for the first time certain matter curves and surfaces using techniques involving prime ideals. The vertical cohomology ring of these fourfolds is calculated for both cases and general formulas for the Euler numbers are derived. Explicit calculations are presented for a specific base B = P-3. We determine the general G(4)-flux that belongs to H-V((2,2)) of the resolved Calabi-Yau fourfolds. As a by-product, we derive for the first time all conditions on G(4)-flux in general F-theory compactifications with a non-holomorphic zero section. These conditions have to be formulated after a circle reduction in terms of Chern-Simons terms on the 3D Coulomb branch and invoke M-theory/F-theory duality. New ChernSimons terms are generated by Kaluza-Klein states of the circle compactification. We explicitly perform the relevant field theory computations, that yield non-vanishing results precisely for fourfolds with a non-holomorphic zero section. Taking into account the new Chern-Simons terms, all 4D matter chiralities are determined via 3D M-theory/F-theory duality. We independently check these chiralities using the subset of matter surfaces we determined. The presented techniques are general and do not rely on toric data.
Ključne besede: flux compactifications, F-theory
Objavljeno: 27.06.2017; Ogledov: 31; Prenosov: 0
.pdf Polno besedilo (1,75 MB)

Black holes with intrinsic spin
Mirjam 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: 46; Prenosov: 0
.pdf Polno besedilo (598,59 KB)

Black hole thermodynamics from a variational principle: asymptotically conical backgrounds
Song-ok 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 2-sphere, 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: M-Theory, Black Holes, String Theory, Gauge-gravity correspondence
Objavljeno: 27.06.2017; Ogledov: 23; Prenosov: 0
.pdf Polno besedilo (834,82 KB)

AdS(2) holographic dictionary
Mirjam Cvetič, Ioannis Papadimitriou, 2016, izvirni znanstveni članek

Opis: We construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This specific model ensures that the dual theory has a well de fined ultraviolet completion in terms of a two dimensional conformal field theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized one-point functions in the presence of arbitrary sources, and derive the asymptotic symmetries and the corresponding conserved charges. In both cases we find that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. We further show that the only non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Comp ere, Song and Strominger [1], in agreement with the results of Castro and Song [2]. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS(2) x S-2 or conformally AdS(2) x S-2 solutions of the STU model in four dimensions, including non extremal black holes. The four dimensional solutions obtained by uplifting the running dilaton solutions coincide with the so called 'subtracted geometries', while those obtained from the uplift of the constant dilaton ones are new.
Ključne besede: 2D gravity, AdS-CFT correspondence, black holes, space-time symmetries
Objavljeno: 27.06.2017; Ogledov: 23; Prenosov: 0
.pdf Polno besedilo (1,01 MB)

On the solvability of second-order impulsive differential equations with antiperiodic boundary value conditions
Yepeng Xing, Valery Romanovski, 2008, izvirni znanstveni članek

Opis: We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.
Ključne besede: second-order impulsive differential equations, antiperiodic boundary value conditions, Green's function
Objavljeno: 26.06.2017; Ogledov: 56; Prenosov: 0
.pdf Polno besedilo (241,29 KB)

Some basic difference equations of Schrodinger boundary value problems
Andreas Ruffing, Maria Meiler, Andrea Bruder, 2009, izvirni znanstveni članek

Opis: We consider special basic difference equations which are related to discretizations of Schrödinger equations on time scales with special symmetry properties, namely, so-called basic discrete grids. These grids are of an adaptive grid type. Solving the boundary value problem of suitable Schrödinger equations on these grids leads to completely new and unexpected analytic properties of the underlying function spaces. Some of them are presented in this work.
Ključne besede: differential equations, discretization, Schrödinger equations, value problems
Objavljeno: 26.06.2017; Ogledov: 18; Prenosov: 0
.pdf Polno besedilo (278,92 KB)

Oscillatory difference equations and moment problems
José M. Ferreira, Sandra Pinelas, Andreas Ruffing, 2014, izvirni znanstveni članek

Opis: In this paper, we first consider some new oscillatory results with respect to the discrete Hermite polynomials of type I, respectively, type II and the Heim-Lorek polynomials. In the second part, we investigate the oscillatory and boundedness properties of the related orthogonality measures and the functions representing them. The polynomials considered so far in this article are closely related to the concept of theWess-Ruffing discretization.
Ključne besede: difference equations, Hermite polynomials, polynomials, discretization
Objavljeno: 26.06.2017; Ogledov: 18; Prenosov: 0
.pdf Polno besedilo (331,56 KB)

Difference-differential operators for basic adaptive discretizations and their central function systems
Lucia Birk, Sophia Roßkopf, Andreas Ruffing, 2012, izvirni znanstveni članek

Opis: The concept of inherited orthogonality is motivated and an optimality statement for it is derived. Basic adaptive discretizations are introduced. Various properties of difference operators which are directly related to basic adaptive discretizations are looked at. A Lie-algebraic concept for obtaining basic adaptive discretizations is explored. Some of the underlying moment problems of basic difference equations are investigated in greater detail.
Ključne besede: discretization, difference operator, Lie algebra, difference equations
Objavljeno: 26.06.2017; Ogledov: 19; Prenosov: 0
.pdf Polno besedilo (408,24 KB)

Comparing algebraic and numerical solutions of classical diffusion process equations in computational financial mathematics
Andreas Ruffing, Patrick Windpassinger, Stefan Panig, 2001, izvirni znanstveni članek

Opis: We revise the interrelations between the classical Black Scholes equation, the diffusion equation and Burgers equation. Some of the algebraic properties the diffusion equation shows are elaborated and qualitatively presented. The related numerical elementary recipes are briefly elucidated in context of the diffusion equation. The quality of the approximations to the exact solutions is compared throughout the visualizations. The article mainly is based on the pedagogical style of the presentations to the Novacella Easter School 2000 on Financial Mathematics.
Ključne besede: diffusion processes, diffusion equations
Objavljeno: 14.06.2017; Ogledov: 19; Prenosov: 0
.pdf Polno besedilo (2,80 MB)

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