Quantum Holonomies in (2+1)-Dimensional Gravity

We describe an approach to the quantisation of (2+1)-dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q-commutation relation. Solutions of diagonal and upper-triangular form are constructed, which in the latter case exhibit additional, non-trivial internal relations for each holonomy matrix. Representations are constructed and a group of transformations - a quasi-modular group - which preserves this structure, is presented.Comment: 10 pages Latex no figure

Normal ordering and boundary conditions for fermionic string coordinates

We build up normal ordered products for fermionic open string coordinates consistent with boundary conditions. The results are obtained considering the presence of antisymmetric tensor fields. We find a discontinuity of the normal ordered products at string endpoints even in the absence of the background. We discuss how the energy momentum tensor also changes at the world-sheet boundary in such a way that the central charge keeps the standard value at string end points.Comment: In this revised version we clarify the issue of consistency between supersymmetry and boundary conditions and stress the fact that we are considering flat space. we also add two more reference

Fermionic anticommutators for open superstrings in the presence of antisymmetric tensor field

We build up the anticommutator algebra for the fermionic coordinates of open superstrings attached to branes with antisymmetric tensor fields. We use both Dirac quantization and the symplectic Faddeev Jackiw approach. In the symplectic case we find a way of generating the boundary conditions as zero modes of the symplectic matrix by taking a discretized form of the action and adding terms that vanish in the continuous limit. This way boundary conditions can be handled as constraints.Comment: Revision: passage from discrete to continuous clarified, comment on previous results using Dirac quantization included, typos corrected. Version to appear in Phys. Lett.

A superspace formulation of the BV action

We show that the BV (Batalin Vilkovisky) action, formulated with an extended BRST symmetry (including the shift symmetry), is also invariant under an extended anti-BRST transformation (where the antifields are the parameters of the transformation), when the gauge fixing Lagrangian is both BRST and anti-BRST invariant. We show that for a general gauge fixing Lagrangian, the BV action can be written in a manifestly extended BRST invariant manner in a superspace with one Grassmann coordinate whereas it can be expressed in a manifestly extended BRST and anti-BRST invariant manner in a superspace with two Grassmann coordinates when the gauge fixing Lagrangian is invariant under both BRST and anti-BRST transformations.Comment: 20 page

Canonical Transformations and Gauge Fixing in the Triplectic Quantization

We show that the generators of canonical transformations in the triplectic manifold must satisfy constraints that have no parallel in the usual field antifield quantization. A general form for these transformations is presented. Then we consider gauge fixing by means of canonical transformations in this Sp(2) covariant scheme, finding a relation between generators and gauge fixing functions. The existence of a wide class of solutions to this relation nicely reflects the large freedom of the gauge fixing process in the triplectic quantization. Some solutions for the generators are discussed. Our results are then illustrated by the example of Yang Mills theory.Comment: A new section about the cohomological approach to the extended BRST quantization has been included. Some new references were added too. Final version to appear in Nucl. Phys.B. 12 pages, LATE

Bulk versus boundary quantum states

An explicit holographic correspondence between $AdS$ bulk and boundary quantum states is found in the form of a one to one mapping between scalar field creation/annihilation operators. The mapping requires the introduction of arbitrary energy scales and exhibits an ultraviolet-infrared duality: a small regulating mass in the boundary theory corresponds to a large momentum cutoff in the bulk. In the massless (conformal) limit of the boundary theory the mapping covers the whole field spectrum of both theories. The mapping strongly depends on the discretization of the field spectrum of compactified $AdS$ space in Poincare coordinates.Comment: Minor changes in the text. Typos correction. References added. Version to appear in Phys. Lett.

QCD/String holographic mapping and high energy scattering amplitudes

We find a one to one mapping between low energy string dilaton states in AdS bulk and high energy glueball states on the corresponding boundary. This holographic mapping leads to a relation between bulk and boundary scattering amplitudes. From this relation and the dilaton action we find the appropriate momentum scaling for high energy QCD amplitudes at fixed angles.Comment: Minor changes in text. Version accepted for publication in PL

Holographic model for dilepton production in p-p collisions

We propose a holographic model for dilepton production in proton-proton collisions based on the exchange of vector mesons. The holographic hard wall model is used to describe the dynamics and interactions of vector mesons and baryons. We estimate the parameters lambda, mu, nu that characterize the angular distribution of the produced dileptons in a region of q_T^2 << Q^2, where perturbative QCD presents an effective strong coupling due to large logarithm corrections.Comment: Revision: V4 In this version we modified the dimension of the fermionic operator to match the canonical dimension of a baryonic operator. This modification affected slightly our results with respect to v3. 25 pages, 3 Latex figures + 6 eps figures, 5 tables. To appear in Nucl. Phys.