Second-Order Five-Dimensional Chern–Simons Gravity

Continuing our previous discussion of the canonical covariant formalism (Zandron, O. S. (in press). International Journal of Theoretical Physics), the second-order canonical fünfbein formalism of the topological five-dimensional Chern–Simons gravity is constructed. Since this gravity model naturally contains a Gauss–Bonnet term quadratic in curvature, the second-order formalism requires the implementation of the Ostrogradski transformation in order to introduce canonical momenta. This is due to the presence of second time-derivatives of the fünfbein field. By performing the space–time decomposition of the manifold M ⁵, the set of first-class constraints that determines all the Hamiltonian gauge symmetries can be found. The total Hamiltonian as generator of time evolution is constructed, and the apparent gauge degrees of freedom are unambiguously removed, leaving only the physical ones.     

Notes on non-commutative Chern–Simons quantum mechanics

The European Physical Journal C - We investigate the classical and quantum aspects of non-commutative topological (Chern–Simons) mechanics. We introduce the magnetic field by the minimal...     

Self-dual Chern–Simons Vortices on Bounded Domains

In this Letter we consider the Abelian Chern–Simons vortices on a bounded simply connected domain. We establish the existence of solutions for the self-duality equations. We prove the uniqueness of solutions when all the vortex points are equal and the domain is star-shaped. We also show the radial symmetry of solutions on balls centered at the vortex point.     

Chern–Simons Action on a Finite Point Space

We apply Connes' noncommutative geometry to a finite point space. The explicit Chern–Simons action on this finite point space is obtained.     

Topological boundary conditions in abelian Chern–Simons theory

We study topological boundary conditions in abelian Chern–Simons theory and line operators confined to such boundaries. From the mathematical point of view, their relationships are described by a certain 2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern–Simons couplings). We argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group classifying bulk line operators (the discriminant group). We describe properties of boundary line operators; in particular we compute the boundary associator. We also study codimension one defects (surface operators) in abelian Chern–Simons theories. As an application, we obtain a classification of such theories up to isomorphism, in general agreement with the work of Belov and Moore.     

String-inspired Chern–Simons modified gravity in four dimensions

Field equations of the Chern–Simons modified gravity in four dimensions are obtained by a truncation of the field equations of the low energy effective string models with first order corrections in the string constant included.     

Domain walls in a generalized Chern–Simons model

In this paper we study the structure of one dimensional topological solitons in a generalized Abelian-Higgs Chern–Simons model where the kinetic term is non-canonical. We present an example of an analytical self-dual electrically charged soliton solution which has a finite momentum per unit length along its direction. We compared the physical properties of our soliton with those for wall of Jackiw–Lee–Weinberg wall presented in Jackiw et al. (Phys. Rev. D 42:3488, 1990) to conclude that the non-canonical kinetic term can make the wall “thicker” redistributing uniformly the momentum flow along it.     

Conformal anomaly,virasoro algebra and Chern—Simons cohomology

We make use of Chern-Simons cohomology and the family index theorem to deal with two-dimensional anomalies, infinite-dimensional algebras and their relations. We also take advantage of Zweibein formulation to treat the world sheet trace anomaly and Virasoro algebra in Polyakov string and to show how the anaomaly-free condition gives rise to the critical dimensions.     

Link invariants and combinatorial quantization of hamiltonian Chern Simons theory

We define and study the properties of observables associated to any link in ×R (where is a compact surface) using the combinatorial quantization of hamiltonian Chern-Simons theory. These observables are traces of holonomies in a non-commutative Yang-Mills theory where the gauge symmetry is ensured by a quantum group. We show that these observables are link invariants taking values in a non-commutative algebra, the so-called Moduli Algebra. When =S ² these link invariants are pure numbers and are equal to Reshetikhin-Turaev link invariants.Laboratoire Propre du CNRS UPR 14.     

Variational Derivation of Exact Skein Relations from Chern–Simons Theories

The expectation value of a Wilson loop in a Chern–Simons theory is a knot invariant. Its skein relations have been derived in a variety of ways, including variational methods in which small deformations of the loop are made and the changes evaluated. The latter method is only allowed to obtain approximate expressions for the skein relations. We present a generalization of this idea that allows to compute the exact form of the skein relations. Moreover, it requires to generalize the resulting knot invariants to intersecting knots and links in a manner consistent with the Mandelstam identities satisfied by the Wilson loops. This allows for the first time to derive the full expression for knot invariants that are suitable candidates for quantum states of gravity (and supergravity) in the loop representation. The new approach leads to several new insights in intersecting knot theory, in particular the role of non-planar intersections and intersections with kinks. Received: 15 March 1996 / Accepted: 8 October 1996     

Exotic RG flows from holography

Holographic RG flows are studied in an Einstein‐dilaton theory with a general potential. The superpotential formalism is utilized in order to characterize and classify all solutions that are associated with asymptotically AdS space‐times. Such solutions correspond to holographic RG flows and are characterized by their holographic β‐functions. Novel solutions are found that have exotic properties from a RG point‐of view. Some have β‐functions that are defined patch‐wise and lead to flows where the β‐function changes sign without the flow stopping. Others describe flows that end in non‐neighboring extrema in field space. Finally others describe regular flows between two minima of the potential and correspond holographically to flows driven by the VEV of an irrelevant operator in the UV CFT.     

Solitons of the Self-dual Chern–Simons Theory on a Cylinder

We study the self-dual Chern–Simons Higgs theory on an asymptotically flat cylinder. A topological multivortex solution is constructed and the fast decaying property of solutions is proved.     

Fractional Spin of System with Chern–Simons Term Coupled to Polaron

The fractional spin of a system with Chern–Simons (CS) term coupled to a polaron at the quantum level is studied. The Faddeev–Senjanovic (FS) scheme for path-integral quantization of constrained Hamiltonian systems is applied. The quantal conserved angular momentum and the fractional spin at the quantum level of this system are presented based on the quantal Noether theorem. The fractional spin is also presented for the system with Maxwell kinetic term.     

Quantum Symmetry of a Chern–Simons System Coupled to a Polaron

The property of fractional spin of the system with Chern–Simons (CS) term coupled to polaron at the quantum level is studied. According to the rule of path integral quantization for constrained Hamiltonian system in Faddeev–Senjanovic (FS) scheme, this system is quantized. Based on the quantal Noether theorem, the quantal conserved angular momentum and the fractional spin at the quantum level of this system is presented. The fractional spin is also presented in the system including Maxwell kinetic term.     

Topological Five-Dimensional Chern–Simons Gravity Theory in the Canonical Covariant Formalism

The canonical covariant formalism (CCF) of the topological five-dimensional Chern–Simons gravity is constructed. Because this gravity model naturally contains a Gauss–Bonnet term, the extended CCF valid for higher curvature gravity must be used. In this framework, the primary constraint and the total Hamiltonian are found. By using the equations of the CCF, it is shown that the bosonic five-form which defines the total Hamiltonian is a first-class dynamical quantity strongly conserved. In this context the equations of motion are also analyzed. To determine the effective interactions of the model, the toroidal dimensional reduction of the five-dimensional Chern–Simons gravity is carried out. Finally the first-order CCF and the usual canonical vierbein formalism (CVF) are related and the Hamiltonian as generator of time evolution is constructed in terms of the first-class constraints of the coupled system.     

Energy Spectrum of Excitations in the Proca–Chern–Simons System

We quantize the Proca–Chern–Simonssystem via the path-integral approach and diagonalizethe Hamiltonian by canonical transformations. We findthat the mass spectrum of the system is equivalent to asystem of two free scalar fields; the statisticalpartition function, which does not exhibit any exoticproperties, is also evaluated from the diagonalizedHamiltonian.     

On Vortex Dynamics in the Self-Dual Chern–Simons–Higgs System

The dynamics of n vortices in the self-dual Chern–Simons–Higgs system defined on the infinite plane is investigated. In adiabatic approximation, the vortex dynamics is determined by considering a rigid motion of a vortex configuration and a motion around a fixed center of mass. A motion of two vortices is studied in detail.     

Self-dual Vortices in a Maxwell–Chern–Simons Model with Non-minimal Coupling

We study self-dual vortex solutions in a Maxwell – Chern – Simons model with anomalous magnetic moment. We establish the existence of multivortex solutions and obtain the quantized energy and the magnetic flux. We also prove the uniqueness of solutions when there is only one vortex point.