Completeness of Wilson loop functionals on the moduli space of SL(2,C)SL(2,C) and SU(1,1)SU(1,1)-connections

The structure of the moduli spaces \M := \A/\G of (all, not just flat) $SL(2,C)$ and $SU(1,1)$ connections on a n-manifold is analysed. For any topology on the corresponding spaces \A of all connections which satisfies the weak requirement of compatibility with the affine structure of \A, the moduli space \M is shown to be non-Hausdorff. It is then shown that the Wilson loop functionals --i.e., the traces of holonomies of connections around closed loops-- are complete in the sense that they suffice to separate all separable points of \M. The methods are general enough to allow the underlying n-manifold to be topologically non-trivial and for connections to be defined on non-trivial bundles. The results have implications for canonical quantum general relativity in 4 and 3 dimensions.Comment: Plain TeX, 7 pages, SU-GP-93/4-

CR Structures and Asymptotically Flat Space-Times

We discuss the unique existence, arising by analogy to that in algebraically special space-times, of a CR structure realized on null infinity for any asymptotically flat Einstein or Einstein-Maxwell space-time.Comment: 6 page

Tensors Mesons in AdS/QCD

We explore tensor mesons in AdS/QCD focusing on f2 (1270), the lightest spin-two resonance in QCD. We find that the f2 mass and the partial width for f2 -> gamma gamma are in very good agreement with data. In fact, the dimensionless ratio of these two quantities comes out within the current experimental bound. The result for this ratio depends only on Nc and Nf, and the quark and glueball content of the operator responsible for the f2; more importantly, it does not depend on chiral symmetry breaking and so is both independent of much of the arbitrariness of AdS/QCD and completely out of reach of chiral perturbation theory. For comparison, we also explore f2 -> pi pi, which because of its sensitivity to the UV corrections has much more uncertainty. We also calculate the masses of the higher spin resonances on the Regge trajectory of the f2, and find they compare favorably with experiment.Comment: 21 pages, 1 figure; Li's correcte

Normal-superfluid interaction dynamics in a spinor Bose gas

Coherent behavior of spinor Bose-Einstein condensates is studied in the presence of a significant uncondensed (normal) component. Normal-superfluid exchange scattering leads to a near-perfect local alignment between the spin fields of the two components. Through this spin locking, spin-domain formation in the condensate is vastly accelerated as the spin populations in the condensate are entrained by large-amplitude spin waves in the normal component. We present data evincing the normal-superfluid spin dynamics in this regime of complicated interdependent behavior.Comment: 5 pages, 4 fig

Directional optical switching and transistor functionality using optical parametric oscillation in a spinor polariton fluid

Over the past decade, spontaneously emerging patterns in the density of polaritons in semiconductor microcavities were found to be a promising candidate for all-optical switching. But recent approaches were mostly restricted to scalar fields, did not benefit from the polariton's unique spin-dependent properties, and utilized switching based on hexagon far-field patterns with 60{\deg} beam switching (i.e. in the far field the beam propagation direction is switched by 60{\deg}). Since hexagon far-field patterns are challenging, we present here an approach for a linearly polarized spinor field, that allows for a transistor-like (e.g., crucial for cascadability) orthogonal beam switching, i.e. in the far field the beam is switched by 90{\deg}. We show that switching specifications such as amplification and speed can be adjusted using only optical means

The Wilsonian Renormalization Group in Randall-Sundrum 1

We find renormalization group transformations for the compactified Randall-Sundrum scenario by integrating out an infinitesimal slice of ultraviolet degrees of freedom near the Planck brane. Under these transformations the coefficients of operators on the Planck brane experience RG evolution. The extra-dimensional radius also scales, flowing to zero in the IR. We find an attractive fixed point in the context of a bulk scalar field theory. Calculations are simplified in the low energy effective theory as we demonstrate with the computation of a loop diagram.Comment: 19 pages, typos adde

Lorentz Symmetry in QFT on Quantum Bianchi I Space-Time

We develop the quantum theory of a scalar field on LQC Bianchi I geometry. In particular, we focus on single modes of the field: the evolution equation is derived from the quantum scalar constraint, and it is shown that the same equation can be obtained from QFT on an "classical" effective geometry. We investigate the dependence of this effective space-time on the wavevector of the mode (which could in principle generate a deformation in local Lorentz-symmetry), focusing our attention on the dispersion relation. We prove that when we disregard backreaction no Lorentz-violation is present, despite the effective metric being different than the classical Bianchi I one. A preliminary analysis of the correction due to inclusion of backreaction is briefly discussed in the context of Born-Oppenheimer approximation.Comment: 14 pages, v3. Corrected a reference in the bibliograph

Automorphism covariant representations of the holonomy-flux *-algebra

We continue an analysis of representations of cylindrical functions and fluxes which are commonly used as elementary variables of Loop Quantum Gravity. We consider an arbitrary principal bundle of a compact connected structure group and following Sahlmann's ideas define a holonomy-flux *-algebra whose elements correspond to the elementary variables. There exists a natural action of automorphisms of the bundle on the algebra; the action generalizes the action of analytic diffeomorphisms and gauge transformations on the algebra considered in earlier works. We define the automorphism covariance of a *-representation of the algebra on a Hilbert space and prove that the only Hilbert space admitting such a representation is a direct sum of spaces L^2 given by a unique measure on the space of generalized connections. This result is a generalization of our previous work (Class. Quantum. Grav. 20 (2003) 3543-3567, gr-qc/0302059) where we assumed that the principal bundle is trivial, and its base manifold is R^d.Comment: 34 pages, 1 figure, LaTeX2e, minor clarifying remark