123284560
Algebras of the Virasoro, Neveu-Schwarz, and Ramond Types on Genus g Riemann Surfaces
During the last few years much work has been devoted to trying to reconcile the operator formalism in conformal field theory and string theory, which was originally formulated in the complex plane, with the fact that in Polyakov string theory Riemann surfaces of arbitrary genus must be taken into account. Also, independently of any string interpretation, it is interesting to know the features of a conformal field theory on a Riemann surface of genus g, and therefore it is important to have a manageable operator formalism for any genus. In two recent papers [1, 2] Krichever and Novikov have introduced a new general formalism that may prove very important in this sense. The basic ingredient in their approach is a discrete basis for the algebra of meromorphic vector fields over a Riemann surface that are holomorphic outside two distinguished points. The basis elements form a closed algebra, which is referred to as the Krichever-Novikov (KN) algebra.
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
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.
117730967
Generalized Wess-Zumino terms and global anomalies in string sigma models
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.
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.
119288395
A new approach to non-commutative inflation
We propose an inflationary scenario inspired by a recent formulation, in terms of coherent states, of non-commutative quantum field theory. We consider the semiclassical Einstein equations, and exploit the ultraviolet finiteness of the non-commutative propagator to construct the expectation value of the energy–momentum tensor associated with a generic scalar field. It turns out that the latter is always finite and dominated by an effective cosmological constant. By combining this general feature with the intrinsic fuzziness of spacetime, we show that non-commutativity governs the energy density of the early Universe in such a way that the strong energy condition is violated. Thus, there might be a bounce and a subsequent inflationary phase, which does not need any ad hoc scalar field.
14243157
Pre-Big Bang scenario on self-T-dual bouncing branes
We consider a new class of five-dimensional dilatonic actions which are invariant under T-duality transformations along three compact coordinates, provided that an appropriate potential is chosen. We show that the invariance remains when we add a boundary term corresponding to a moving 3-brane, and we study the effects of the T-duality symmetry on the brane cosmological equations. We find that T-duality transformations in the bulk induce scale factor duality on the brane, together with a change of sign of the pressure of the brane cosmological matter. However, in a remarkable analogy with the Pre-Big Bang scenario, the cosmological equations are unchanged. Finally, we propose a model where the dual phases are connected through a scattering of the brane induced by an effective potential. We show how this model can realize a smooth, non-singular transition between a pre-Big Bang superinflationary Universe and a post-Big Bang accelerating Universe.
16251449
Brane world in a topological black hole bulk
We consider a static brane in the background of a topological black hole in arbitrary dimensions. For hyperbolic horizons, we find a solution only when the black hole mass assumes its minimum negative value. In this case, the tension of the brane vanishes, and the brane position coincides with the location of the horizon. For an elliptic horizon, we show that the massless mode of Randall–Sundrum is recovered in the limit of large black hole mass.
117021213
Studying the neutron orbital structure by coherent hard exclusive processes off 3He
Hard exclusive processes, such as Deeply Virtual Compton Scattering (DVCS), allow to access generalized parton distributions (GPDs). By means of an Impulse Approximation (IA) calculation, it is shown here how, in the low momentum transfer region, the sum of the GPDs H and E is dominated by the neutron contribution. Thanks to this property, 3He could open a new way to access the neutron structure information. In this work, a simple and efficient extraction procedure of the neutron GPDs, able to take into account the nuclear effects included in IA analysis, is proposed.