16014102
Four-Dimensional Yang–Mills Theory as a Deformation of Topological BF Theory
Abstract:The classical action for pure Yang–Mills gauge theory can be formulated as a deformation of the topological BF theory where, beside the two-form field B, one has to add one extra-field η given by a one-form which transforms as the difference of two connections. The ensuing action functional gives a theory that is both classically and quantistically equivalent to the original Yang–Mills theory. In order to prove such an equivalence, it is shown that the dependency on the field η can be gauged away completely. This gives rise to a field theory that, for this reason, can be considered as semi-topological or topological in some but not all the fields of the theory. The symmetry group involved in this theory is an affine extension of the tangent gauge group acting on the tangent bundle of the space of connections. A mathematical analysis of this group action and of the relevant BRST complex is discussed in detail.
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.
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.
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.
9318966
Toroidal black holes and T-duality
Abstract We consider the toroidal black holes that arise as a generalization of the AdS5×S5 solution of type IIB supergravity. The symmetries of the horizon space allow T-duality transformations that can be exploited to generate new inequivalent black hole solutions of both type IIB and type IIA supergravity, with non-trivial dilaton, B-field, and RR-forms. We examine the asymptotic structure and thermodynamical properties of these solutions.
53531318
PARTICLE PRODUCTION AND TRANSPLANCKIAN PROBLEM ON THE NONCOMMUTATIVE PLANE
We consider the coherent state approach to noncommutativity and we derive from it an effective quantum scalar field theory. We show how the noncommutativity can be taken into account by a suitable modification of the Klein–Gordon product, and of the equal-time commutation relations. We prove that, in curved space, the Bogoliubov coefficients are unchanged, hence the number density of the produced particle is the same as for the commutative case. What changes though is the associated energy density, and this offers a simple solution to the transplanckian problem.
118638108
Superluminal dispersion relations and the Unruh effect
In the context of quantum gravity phenomenology, we study the Unruh effect in the presence of superluminal dispersion relations. In particular, we estimate the response function and the probability rate for an accelerated detector coupled to a massless scalar field, whose dispersion relation becomes essentially quadratic beyond a threshold momentum ${k}_{p}$. By means of a perturbative analysis, we show that superluminal dispersion induces a correction to the Planckian spectrum, which tends to vanish as ${k}_{p}$ increases.
118521890
Neutron orbital structure from generalized parton distributions of 3He
The generalized parton distribution H and E of the 3He nucleus, which could be measured in hard exclusive processes, such as coherent deeply virtual Compton scattering, are thoroughly analyzed in impulse approximation, within the Av18 interaction. It is found that their sum is dominated to a large extent by the neutron contribution: The peculiar spin structure of 3He makes this target unique for the extraction of the neutron information. This observation could allow to access for the first time, in dedicated experiments, the orbital angular momentum of the partons in the neutron.
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.