Search results for "model theory"
showing 10 items of 681 documents
The Complete Solution of the Classical SL(2,ℝ/U(1) Gauged WZNW Field Theory
1998
We prove that any gauged WZNW model has a Lax pair representation, and give explicitly the general solution of the classical equations of motion of the SL(2,R)/U(1) theory. We calculate the symplectic structure of this solution by solving a differential equation of the Gelfand-Dikii type with initial state conditions at infinity, and transform the canonical physical fields non-locally onto canonical free fields. The results will, finally, be collected in a local B\"acklund transformation. These calculations prepare the theory for an exact canonical quantization.
The quantum clock: a critical discussion on space-time
2016
We critically discuss the measure of very short time intervals. By means of a Gedankenexperiment, we describe an ideal clock based on the occurrence of completely random events. Many previous thought experiments have suggested fundamental Planck-scale limits on measurements of distance and time. Here we present a new type of thought experiment, based on a different type of clock, that provide further support for the existence of such limits. We show that the minimum time interval $\Delta t$ that this clock can measure scales as the inverse of its size $\Delta r$. This implies an uncertainty relation between space and time: $\Delta r$ $\Delta t$ $> G \hbar / c^4$; where G, $\hbar$ and c are …
The geometry of N=3 AdS4 in massive IIA
2018
The geometry of the ${\cal N} = 3$, SO(4)--invariant, AdS$_4$ solution of massive type IIA supergravity that uplifts from the ${\cal N} = 3 $ vacuum of $D=4$ ${\cal N} = 8$ dyonic ISO(7) supergravity is investigated. Firstly, a $D=4$, SO(4)--invariant restricted duality hierarchy is constructed and used to uplift the entire, dynamical SO(4)--invariant sector to massive type IIA. The resulting consistent uplift formulae are used to obtain a new local expression for the ${\cal N} = 3 $ AdS$_4$ solution in massive IIA and analyse its geometry. Locally, the internal $S^6$ geometry corresponds to a warped fibration of $S^2$ and a hemisphere of $S^4$. This can be regarded as a warped generalisati…
On AdS7 stability
2019
AdS$_7$ supersymmetric solutions in type IIA have been classified, and they are infinitely many. Moreover, every such solution has a non-supersymmetric sister. In this paper, we study the perturbative and non-perturbative stability of these non-supersymmetric solutions, focusing on cases without orientifolds. Perturbatively, we first look at the KK spectrum of spin-2 excitations. This does not exhibit instabilities, but it does show that there is no separation of scales for either the BPS and the non-BPS case, thus proving for supersymmetric AdS$_7$ a well-known recent conjecture. We then use 7d gauged supergravity and a brane polarization computation to access part of the spectrum of KK sc…
Wilson Loop Form Factors: A New Duality
2017
We find a new duality for form factors of lightlike Wilson loops in planar $\mathcal N=4$ super-Yang-Mills theory. The duality maps a form factor involving an $n$-sided lightlike polygonal super-Wilson loop together with $m$ external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality. However there are some crucial subtleties with the cancellation of spurious poles due to the gauge fixing. They are resolved by finding the correct formulation of the Wilson loop and by careful analyti…
Small and hollow magnetic monopoles
2018
We deal with the presence of magnetic monopoles in a non Abelian model that generalizes the standard 't~Hooft-Polyakov model in three spatial dimensions. We investigate the energy density of the static and spherically symmetric solutions to find first order differential equations that solve the equations of motion. The system is further studied and two distinct classes of solutions are obtained, one that can also be described by analytical solutions which is called small monopole, since it is significantly smaller than the standard 't~Hooft-Polyakov monopole. The other type of structure is the hollow monopole, since the energy density is endowed with a hole at its core. The hollow monopole …
Confronting the IR Fixed Point Cosmology with High Redshift Observations
2004
We use high-redshift type Ia supernova and compact radio source data in order to test the infrared (IR) fixed point model of the late Universe which was proposed recently. It describes a cosmology with a time dependent cosmological constant and Newton constant whose dynamics arises from an underlying renormalization group flow near an IR-attractive fixed point. Without any finetuning or quintessence field it yields $\Omega_{\rm M}=\Omega_{\Lambda}=1/2$. Its characteristic $t^{4/3}$-dependence of the scale factor leads to a distance-redshift relation whose predictions are compared both to the supernova and to the radio source data. According to the $\chi^2$ test, the fixed point model reprod…
Hybrid approximation for solutions of high-order integro-differential equations including variable delay
2020
Abstract In this study, a numerical technique with hybrid approximation is developed for solving high-order linear integro-differential equations including variable delay under the initial conditions. These type of problems are of applications in mathematical physics, mechanics, natural sciences, electronics and computer science. The aim of this work is to investigate an approximation with the matrix forms of Taylor and Laguerre polynomials along with standard collocation points. By the reduction of the solution of this problem with regard to the matrix relations, the solution of a system of algebraic equations has been obtained. The usefulness of this algorithm has been demonstrated by num…
Interpretation of EXAFS in scheelite-type AWO4(A = Ca, Sr, Ba) compounds using molecular dynamics simulations
2013
In this work we successfully interpret the W L3-edge EXAFS spectra in scheelite-type AWO4 (A = Ca, Sr, Ba) compounds using a combination of classical NVT molecular dynamics (MD) and ab initio multiple-scattering (MS) theory. The configuration-averaged EXAFS spectra show good agreement with our room temperature experimental data supporting the reliability of the developed force-field models. The contributions from all coordination shells up to 6 A are elucidated. The contribution of the MS effects into the total EXAFS signal in AWO4 compounds is small, being around 10%.
Group theory aspects of chaotic strings
2014
Chaotic strings are a special type of non-hyperbolic coupled map lattices, exhibiting a rich structure of complex dynamical phenomena with a surprising correspondence to physical contents. Chaotic strings are generated by the Chebyshev maps T2() and T3(). In this paper we connect the Chebyshev maps via the Galois theory to the cyclic groups Z2 and Z3 and give some ideas how this fundamental connection might lead to the emergence of the familiar Lie group structure of particle physics and, finally, even to the emergence of space-time. The Z3-graded cubic and ternary algebras presented here have been introduced by R. Kerner in 1991 and then developed and elaborated in collaboration with many …