Workshop on Quantization, Dualities & Integrable Systems VI
In Memoriam: FEZA GÜRSEY
20 - 22 April 2007, METU, Ankara
Abstracts
The Quadratic Symmetric Teleparallel
Gravity in Two-Dimensions
Muzaffer Adak
Department of Physics, Faculty of Arts and Sciences,
Pamukkale University, 20100 Denizli, Turkey
Tekin Dereli
Department of Physics, Koç University
34450 Sarıyer-Istanbul, Turkey
Abstract
A 2D symmetric teleparallel gravity model is given by a generic 4-parameter action that is quadratic in thenon-metricity tensor. Variational field equations are derived. A class of conformally flat solutions is given. We also discuss static and cosmological solutions.
Non-anomalous `Ward' identities to supplement large-N multi-matrix loop equations for correlations
Levent Akant, Govind S. Krishnaswami
Abstract
arXiv:hep-th/0611350v1
This work concerns single-trace correlations of Euclidean multi-matrix models. In the large-N limit we show that Schwinger-Dyson equations imply loop equations and non-anomalous Ward identities. Loop equations are associated to generic infinitesimal changes of matrix variables (vector fields). Ward identities correspond to vector fields preserving measure and action. The former are analogous to Makeenko-Migdal equations and the latter to Slavnov-Taylor identities. Loop equations correspond to leading large-N Schwinger-Dyson equations. Ward identities correspond to 1/N^2 suppressed Schwinger-Dyson equations. But they become leading equations since loop equations for non-anomalous vector fields are vacuous. We show that symmetries at infinite N persist at finite N, preventing mixing with multi-trace correlations. For one matrix, there are no non-anomalous infinitesimal symmetries. For two or more matrices, measure preserving vector fields form an infinite dimensional graded Lie algebra, and action preserving ones a subalgebra. For Gaussian, Chern-Simons and Yang-Mills models we identify up to cubic non-anomalous vector fields, though they can be arbitrarily non-linear. Ward identities are homogeneous linear equations. We use them with the loop equations to determine some correlations of these models. Ward identities alleviate the underdeterminacy of loop equations. Non-anomalous symmetries give a naturalness-type explanation for why several linear combinations of correlations in these models vanish.
Electromagnetic Properties of Kerr-AdS Black Holes in Four and Higher Dimensions
Alikram N. Aliev
Abstract
Developments in string/M-theory have greatly stimulated thestudy of black hole solutions
in anti-de Sitter (AdS) space.The intriguingexamples of this come from the AdS/CFT correspondence between a weakly coupled gravity system in an AdS background and a strongly coupled conformal field theory (CFT) on its boundary. Probingthe AdS/CFT correspondencefor rotating Kerr-AdS black holes in the bulk and conformal field theory living on a boundary Einstein universeshows that, in the critical limit in which the rotation of theboundary Einstein universe occurs at the speed of light,the genericthermodynamic features of the bulk/boundary theory are similar.Inspired by this fact, we examine theproperties ofcharged Kerr-AdSblack holes in four and higher spacetime dimensions. Assuming that theKerr-AdS black holes may carry a test electric charge, we construct the exact solutions of the Maxwell equations for associated electromagnetic fields. For this purpose, wepropose an elegant waybased on using the timelike generators in the spacetime underconsideration and in its reference background. We follow withthecalculationof the gyromagnetic ratio for the black holeswith a single angular momentum in all higher dimensions and find a conciseformula which has the following striking features: (i) It shows thatg=2is a universal feature of black holes in four dimensions. (ii) Italso shows that for maximally rotating black holes thegyromagneticratiog=2regardless of the spacetime dimension. This fact has relevance for AdS/CFT correspondence and one may expectthe same valueg=2 for charged conformal matter that is rotating at the speed of light in a boundary Einstein universe.
Spontaneous Symmetry Breaking, Goldstone Theorem, Thin Spectrum
and Excitation Decoherence in Many Body Quantum Systems
T. Birol, T. Dereli and Ö. E. Müstecaplıoğlu
Deparment of Physics, Koç University,
Rumelifeneri Yolu, 34450, Sarıyer, İstanbul, Turkey
Abstract
The concept of spontaneous symmetry breaking is reviewed. The Nambu-Goldstone Theorem, which emerges from this phenomenon, is studied and its effect on phase decoherence of a many-body quantum system is argued. For this, the specific example of a dilute atomic Bose-Einstein condensate is given. In the light of recently-proposed thin spectrum and decoherence relationship, it is shown that excitations of such a system has a finite life time, which is usually shorter than the ground state life time. Final remarks are made on other possible symmetries broken in similar physical systems and their effects on life time of quantum systems in mesoscopic and macroscopic limits.
Noncommutative Supersymmetric Gauge Theories and Seiberg-Witten Map.
Ömer Faruk Dayı
Abstract
Gauge theories in noncommuting and non-anticommuting superspace will be discussed. Then, obtaining ordinary supersymmetric gauge theory from the noncommutative one, in terms of a generalization of the Seiberg-Witten map, will be presented.
Noncommutative Gravity in Six Dimensions
Cemsinan Deliduman
Abstract
arXiv:hep-th/0607096v2
A gauge theory of gravity is defined in 6 dimensional non-commutative space-time. The gauge group is the unitary group U(2,2), which contains the homogeneous Lorentz group, SO(4,2), in 6 dimensions as a subgroup. It is shown that, after the Seiberg-Witten map, in the corresponding theory the lowest order corrections are first order in the non-commutativity parameter \theta. This is in contrast with the results found in non-commutative gauge theories of gravity with the gauge group SO(d,1).
Wigner functions, coherent states and uncertainty structures of
Landau levels in deformation quantization
Bengü Demircioğlu, Abdullah Verçin
Abstract
Phase-space properties of Landau problem are investigated by the generating function method in the autonomous framework of deformation quantization. Characteristics properties of Wigner functions are analyzed by making use of generating function which represents the phase space coherent state function. Two dimensional and onedimensional marginal probability densities are derived and the uncertainty structures of Landau levels, of standard coherent states as well as of generalized coherent states are established.
This talk is based on the following works
1. B. Demircioğlu and A. Verçin 2003,Ann. Phys. (NY) 305 1; arXiv:quant-ph/021115.
2. B. Demircioğlu and A. Verçin 2007, (submitted for publication)
Relevance of Gravitation for the Covariant Description of Electromagnetism in Dielectrics
Tekin Dereli
Department of Physics, Koç University, Istanbul
Abstract
There has been a rapid development in recent years in the construction of"traps" for confining collective states ofmatter on scales intermediate between macro- and micro- dimensions.Condensates of cold atoms and fabricated nano-structures offer many new avenues for technological development when coupled to probes by EM fields.The constitutive properties of such novel material will play an important role in this development.Space science is also progressing rapidly and can provide new laboratory environments with variable gravitation and controlled acceleration in which the properties of such states of matter may be explored. We calculated the form of the phenomenological stress-energy-momentum tensor for the electromagnetic field in a class of inhomogeneous, anisotropic magneto-electric media from first principles in terms of a fully relativistic covariant variational framework. Our results offer a new and efficient way to establish a coherent understanding of the stresses and energy-momentum exchanges induced by electromagnetic interactions with such matter. Supplemented with additional data based on mechanical and elasto-dynamic responses onegains a more confident picture of a total phenomenological symmetric stress-energy-momentum tensor fora wide class of moving media than that based on previous ad-hoc choices.
This talk is based on the joint published work
T.Dereli, J. Gratus, R.W.Tucker, Phys.Lett. A371 (2007) 190-193
It is quoted in Nature News and Views, Vol 444/14 December 2006, p.823
An Exact Solution of the Gauss-Bonnet Gravity
Metin Gürses
Abstract
We give an exact solution of the Einstein-Gauss-Bonnet field equations coupled
with a scalar field.
Characteristic Lie Algebra and Classification of Semi-Discrete Models
Ismagil Habibullin, Aslı Pekcan
Abstract
arXiv:nlin/0610074v2
Characteristic Lie algebras of semi-discrete chains are studied. The attempt to adopt this notion to the classification of Darboux integrable chains has been undertaken.
On the Discreteness and Reality of the Spectrum
for Some Non-Hermitian Hamiltonians
Hüseyin Şirin Hüseyin
Department of Mathematics, Atılım University,
06836 Incek, Ankara, Turkey
E-mail:
Abstract
In recent years, the PT-symmetric operators have attracted considerable attention, because ample numerical and asymptotic studies suggest that many of such operators have real eigenvalues only, even though they are not self-adjoind (Hermitian). In this talk, we review the proof of a conjecture concerning the reality of the spectrum of certain non-Hermitian PT-symmetric quantum mechanical systems.
6D dyonic string with active hyperscalars
Ali Kaya
Abstract
We derive the necessary and sufficient conditions for the existence of a Killing spinor in N=(1,0) gauge supergravity in six dimensions. These are shown to imply most of the field equations. In this framework, we presenta novel 1/8 supersymmetric dyonic string solution with nonvanishing hypermultiplet scalars. The activated scalars parametrize a 4 dimensional submanifold of a quaternionic hyperbolic ball. We employ an identity map between this submanifold and the internal spacetransverse to the string worldsheet. The basic properties of thesolution are discussed.
Towards the Classification of Scalar Non-Polynomial Evolution Equations:Polynomiality in top Three Derivatives
Eti Mizrahi
Abstract
We prove that arbitrary (non-polynomial) scalar evolution equations of order m are
polynomial in the derivatives u_m for m = 0; 1; 2. The proof is based on the integrabilty
test by the existence of a formal symmetry introduced by Mikhailov Shabat and Sokolov
and uses the existence of the canonical conserved densities ρ^(1) and ρ^(3).
Pseudo-Hermitian Quantum Mechanics: Conceptual Implications and Practical Applications
Ali Mostafazadeh
Abstract
We describe how a naïve classical analog of pseudo-Hermitian quantum mechanics connects with the standard classical mechanics, describe the physical content of the quantum system defined by a delta-function potential with a complex coupling, present a simple application of the methods of pseudo-Hermitian quantum mechanics in the description of electromagnetic waves propagating in arbitrary linear media with time-independent positive-definite dielectric and permeability tensors, and (time permitting) show why the recent claim [Bender et al, Phys. Rev. Lett. 98, 040403 (2007)] that PT-symmetric Hamiltonians allow for arbitrarily fast quantum evolutions is completely unfounded.
Quantum Effects on Cosmological Scales
Vakıf Kemal Önemli
Abstract
Present cosmological observations do not exclude the possibility of our universe undergoing a super-accelerated phase of cosmic expansion.Super-acceleration is difficult to explain with classical models onaccount of the problem with stability. The observed persistence of the universe, therefore, can only be consistent with a relatively brief,self-limiting phase of super-acceleration. One way to get such aphase, without violating classical stability, is via quantum effects.Quantum effects are enhanced during inflation for particles that are effectively massless and classically conformally non-invariant; i.e. for gravitons and massless minimally coupled (MMC) scalars. Thus, we naturally consider MMC scalar with a quartic self-interaction in the locally de Sitter background of an inflating universe of arbitrary spacetime dimension. Using dimensional regularization we compute the fully renormalized stress-energy tensor and scalar self-mass squared at one- and two-loop order. Our results show that quantum effects can induce a temporary phase of super-acceleration, causing a violation of the weak energy condition (WEC) on cosmological scales---on average, not just in fluctuations. The effect can be understood as follows. Inflationary particle production causes the scalar to undergo a random walk such that its average distance from the minimum of the quartic potential increases without a bound. This increases the vacuum energy which leads to the violation of the WEC by virtue of the stress-energy conservation law. The process is self-limiting because, inflationary particle production gets smaller as the field grows, since it develops a positive mass (the curvature associated with being away from the minimum of the potential) that cuts off the particle production. Moreover, as the scalar rises up its potential the classical restoring force pushes it back down. Hence, the field can not continue to rollup its position. It must eventually come to a halt. The maximuminduced scalar self-mass squared remains perturbatively small andpositive; it does not go tachyonic. Thus, the system is stable.
Topologically massive gravity as a Pais-Uhlenbeck oscillator
Özgür Sarıoğlu, Bayram Tekin
Abstract
arXiv:gr-qc/0608085v2
We give a detailed account of the free field spectrum and the Newtonian limit of the linearized "massive" (Pauli-Fierz), "topologically massive" (Einstein-Hilbert-Chern-Simons) gravity in 2+1 dimensions about a Minkowski spacetime. For a certain ratio of the parameters, the linearized free theory is Jordan-diagonalizable and reduces to a degenerate "Pais-Uhlenbeck" oscillator which, despite being a higher derivative theory, is ghost-free.
Gravitational charges of transverse asymptotically AdS spacetimes
Hakan Cebeci, Bayram Tekin, Özgür Sarıoğlu
Abstract
arXiv:hep-th/0611011v3
Using Killing-Yano symmetries, we construct conserved charges of spacetimes that asymptotically approach to the flat or Anti-de Sitter spaces only in certain directions. In D dimensions, this allows one to define gravitational charges (such as mass and angular momenta densities) of p-dimensional branes/solitons or any other extended objects that curve the transverse space into an asymptotically flat or AdS one. Our construction answers the question of what kind of charges the antisymmetric Killing-Yano tensors lead to.
Construction of certain reducible Spin(7) invariant
8-manifolds
Ayşe Hümeyra Bilge, Selman Uğuz
Abstract
A manifold M with Spin(7) holonomy group, or simply a Spin(7) manifold,can be characterized by the existence of the Bonan 4-form Ω. The purpose ofthis work is to study certain reducible manifolds with Spin(7) holonomy by usingvolume-preserving vector fields. We will see that these vector fields induce theBonan 4-form on 8-dimensional manifolds. We give the construction of metricswith Spin(7) holonomy group. The metrics are constructed from the solutions tothe first-order differential equations for the volume-preserving vector fields. In thiswork, the manifold under consideration is R^2 X S^3 X S^3, which is paralellizable. TheSpin(7) invariant metric which is given in Y.Yasui, T. Ootsuka ( C.Q.G. (2001))on this manifold is obtained by solving these differential equations.
Dimensional Reduction, Seiberg--Witten Map and Supersymmetry
E. Ulaş Saka, Kayhan Ülker
Abstract
arXiv:hep-th/0701178v2
It is argued that dimensional reduction of Seiberg-Witten map for a gauge field induces Seiberg-Witten maps for the other noncommutative fields of a gauge invariant theory. We demonstrate this observation by dimensionally reducing the noncommutative N=1 SYM theory in 6 dimensions to obtain noncommutative N=2 SYM in 4 dimensions. We explicitly derive Seiberg-Witten maps of the component fields in 6 and 4 dimensions. Moreover, we give a general method to define the deformed supersymmetrytransformations that leaves the actions invariant after performing the Seiberg-Witten maps.
Conformal Hyperbolicity of Warped Products
Bülent Ünal
Abstract
We first discuss the concept of conformal hyperbolicity and then investigate the conformal hyperbolicity and conjugate points of standard static space- times. Moreover, we establish an upper bound for the time-like diameter of a Standard static space-time obtainedby the Ricci tensor inequalities.
On integrable boundary conditions for Liouville equation
Kostyantyn Zheltukhin
Abstract
The notion of Lax representation is used to give a definition of integrable boundary conditions. Boundary conditions satisfying the given definition of integrability are found for Liouville equation.
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