121725055
Conformal invariance on a generic Riemann surface in the presence of a non-flat background metric
Abstract By using bases of meromorphic differentials, recently proposed by Krichever and Novikov, we calculate the brackets of the moments of the energy-momentum tensor of a bosonic string theory in the presence of a generic target metric. To do this we expand the target metric in normal coordinates. To the lowest perturbative order we find that the BRST operator is nilpotent if we impose the condition that the Ricci tensor of the target metric vanish.
117142608
On the algebraic structure of link-diagrams on a 2-dimensional surface
Following and generalizing a paper by Turaev, we consider some algebraic structures on the set of (generalized) link-diagrams, meant simply as collections of immersed loops on a two dimensional surface, with the specification of an over/undercrossing prescription at each double point. This definition is general enough to be relevant not only to traditional knot-theory, but possibly to some statistical mechanical models. A coalgebra structure is introduced on some modules (over polynomial rings), generated by these diagrams. The compatibility of this coalgebra structure with the skein invariance and the invariance under Reidemeister moves is discussed. A Hopf algebra structure results only in some special cases, which are thoroughly examined. It is shown that a special choice of the ground (polynomial) ring over which the diagram module is defined, allows us to define link-invariants for links (in the ordinary sense) in Σ×[0,1],where Σ is a (closed or open) two-dimensional surface. These invariants generalize in a nontrivial way the Jones polynomials and the Homfly polynomials (at least when the last ones are computed for some special values of the variables). In a sequel paper the relation between the algebraic structures of link-diagrams, some special types of quantum groups and the quantum holonomy will be discussed.
117730967
Generalized Wess-Zumino terms and global anomalies in string sigma models
119943646
Relation between representations of KN and virasoro algebras
Abstract Some aspects of conformal field theory over Riemann surfaces are examined. We study, in particular, on simple systems (b−c systems) the relation between representations of the Virasoro and the KN algebras. KN algebra representations decompose into an infinite sum of the Virasoro algebra representations. We argue that the KN algebra representations are the right tool in order to classify conformal field theories over higher genus Riemann surfaces.
6392662
Loop and Path Spaces and¶Four-Dimensional BF Theories:¶Connections, Holonomies and Observables
Abstract: We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows.For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A,B).In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non-topological case, the surface terms may be relevant for the understanding of the quark-confinement problem. In the topological case the (perturbative) four-dimensional quantum BF-theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M.
117924192
Generalized wess-zumino terms
8497922
Modified Dispersion Relations and trans-Planckian Physics
We consider modified dispersion relations in quantum field theory on curved space-time. Such relations, despite breaking the local Lorentz invariance at high energy, are considered in several phenomenological approaches to quantum gravity. Their existence involves a modification of the formalism of quantum field theory, starting from the problem of finding the scalar Green's functions up to the renormalization of various quantum expectation values. In this work we consider a simple example of such modifications, in the case of ultra-static metric. We show how to overcome the lack of Lorentz invariance by introducing a preferred frame, with respect to which we can express the Green's functions as an integral over all frequencies of a space-dependent function. The latter can be expanded in momentum space, and by integrating over all frequencies, we finally find the expansion of the Green's function up to four derivatives of the metric tensor. The relation with the proper-time formalism is also discussed.
119193598
Momentum-space representation of Green's functions with modified dispersion relations on general backgrounds
We consider the problem of calculating the Green's functions associated to a massive scalar field with modified dispersion relations. We analyze the case when dispersion is modified by higher derivative spatial operators acting on the field orthogonally to a preferred direction, determined by a unit timelike vector field. By assuming that the integral curves of the vector field are geodesics, we expand the modified Klein-Gordon equation in Fermi normal coordinates. By means of a Fourier transform, we find a series representation in momentum-space of the Green's functions. The coefficients of the series are geometrical terms containing combinations of the Ricci tensor and the vector field, as expected from previous calculations with different methods and for specific backgrounds.
49385697
INSTALLATION AND COMMISSIONING OF THE RF SYSTEM FOR THE NEW ELETTRA BOOSTER
The commissioning of the new booster of the Elettra synchrotron radiation storage ring started in Fall 2007. The RF system of the booster is made of a five cells accelerating cavity fed by a 60 kW 500 MHz power plant. The accelerating cavity voltage is ramped along with the booster energy at repetition rate 3 Hz. The cavity field is controlled by analog feedback loops on amplitude, phase and the resonant frequency. This paper describes the setting into operation of the system and its performances during the commissioning phase of the machine.
16113420
Self-T-dual brane cosmology and the cosmological constant problem
We consider a codimension-one brane embedded in a gravity-dilaton bulk action, whose symmetries are compatible with T-duality along the space-like directions parallel to the brane, and the bulk time-like direction. The equations of motions in the string frame allow for a smooth background obtained by the union of two symmetric patches of AdS space. The Poincare invariance of the solution appears to hold independently of the value of the brane vacuum energy, through a self-tuning property of the dilaton ground state. Moreover, the effective cosmology displays a bounce, at which the scale factor does not shrink to zero. Finally, by exploiting the T-duality symmetry, we show how to construct an ever-expanding Universe, along the lines of the Pre-Big-Bang scenario.
119287029
ASPECTS OF QUANTUM GRAVITY IN COSMOLOGY
We review some aspects of quantum gravity in the context of cosmology. In particular, we focus on models with a phenomenology accessible to current and near-future observations, as the early Universe might be our only chance to peep through the quantum gravity realm.