Stringy K-theory and the Chern character

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new ring called the full orbifold K-theory of Y. For a global quotient Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra of the full orbifold K-theory of the the stack Y and is linearly isomorphic to the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a different, ``quantum,'' product, which respects the natural group grading. We prove there is a ring isomorphism, the stringy Chern character, from stringy K-theory to stringy cohomology, and a ring homomorphism from full orbifold K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy Grothendieck-Riemann-Roch for etale maps. We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's construction. Since our constructions do not use complex curves, stable maps, admissible covers, or moduli spaces, our results simplify the definitions of Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of Abramovich-Graber-Vistoli's orbifold Chow. We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler Resolution Conjecture holds for symmetric products. Our results hold both in the algebro-geometric category and in the topological category for equivariant almost complex manifolds.Comment: Exposition improved and additional details provided. To appear in Inventiones Mathematica

Topological Orbifold Models and Quantum Cohomology Rings

We discuss the toplogical sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold of ${\bf CP}^1$ by the dihedral group $D_{4},$ how to compute the complete ring of observables. Through this procedure, we compute all the rings from dihedral ${\bf CP}^1$ orbifolds; we note a similarity with rings derived from perturbed $D-$series superpotentials of the $A-D-E$ classification of $N = 2$ minimal models. We then consider ${\bf CP}^2/D_4,$ and show how the techniques of topological-anti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds.Comment: 48 pages, harvmac, HUTP-92/A06

Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory

We study D-branes and Ramond-Ramond fields on global orbifolds of Type II string theory with vanishing H-flux using methods of equivariant K-theory and K-homology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. We emphasize its role as the correct cohomological tool which captures known features of the low-energy effective field theory, and which provides new consistency conditions for fractional D-branes and Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings of D-branes which generalize previous examples. We propose a definition for groups of differential characters associated to equivariant K-theory. We derive a Dirac quantization rule for Ramond-Ramond fluxes, and study flat Ramond-Ramond potentials on orbifolds.Comment: 46 pages; v2: typos correcte

Stability of circular orbits of spinning particles in Schwarzschild-like space-times

Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being constant and normal to the plane of orbits. For the de Sitter background the orbits are always stable with particle velocity and momentum being co-linear along them. The world-line deviation equations for particles of the same spin-to-mass ratios are solved and the resulting deviation vectors are used to study the stability of orbits. It is shown that the orbits are stable against radial perturbations. The general criterion for stability against normal perturbations is obtained. Explicit calculations are performed in the case of the Schwarzschild space-time leading to the conclusion that the orbits are stable.Comment: eps figures, submitted to General Relativity and Gravitatio

Gauge Theory and the Excision of Repulson Singularities

We study brane configurations that give rise to large-N gauge theories with eight supersymmetries and no hypermultiplets. These configurations include a variety of wrapped, fractional, and stretched branes or strings. The corresponding spacetime geometries which we study have a distinct kind of singularity known as a repulson. We find that this singularity is removed by a distinctive mechanism, leaving a smooth geometry with a core having an enhanced gauge symmetry. The spacetime geometry can be related to large-N Seiberg-Witten theory.Comment: 31 pages LaTeX, 2 figures (v3: references added

(Re)constructing Dimensions

Compactifying a higher-dimensional theory defined in R^{1,3+n} on an n-dimensional manifold {\cal M} results in a spectrum of four-dimensional (bosonic) fields with masses m^2_i = \lambda_i, where - \lambda_i are the eigenvalues of the Laplacian on the compact manifold. The question we address in this paper is the inverse: given the masses of the Kaluza-Klein fields in four dimensions, what can we say about the size and shape (i.e. the topology and the metric) of the compact manifold? We present some examples of isospectral manifolds (i.e., different manifolds which give rise to the same Kaluza-Klein mass spectrum). Some of these examples are Ricci-flat, complex and K\"{a}hler and so they are isospectral backgrounds for string theory. Utilizing results from finite spectral geometry, we also discuss the accuracy of reconstructing the properties of the compact manifold (e.g., its dimension, volume, and curvature etc) from measuring the masses of only a finite number of Kaluza-Klein modes.Comment: 23 pages, 3 figures, 2 references adde

Absolute Proper Motions to B~22.5: IV. Faint, Low Velocity White Dwarfs and the White Dwarf Population Density Law

The reduced proper motion diagram (RPMD) for a complete sample of faint stars with high accuracy proper motions in the North Galactic Pole field SA57 is investigated. Eight stars with very large reduced proper motions are identified as faint white dwarf candidates. We discriminate these white dwarf candidates from the several times more numerous QSOs based on proper motion and variability. We discuss the implausibility that these stars could be any kind of survey contaminant. If {\it bona fide} white dwarfs, the eight candidates found here represent a portion of the white dwarf population hitherto uninvestigated by previous surveys by virtue of the faint magnitudes and low proper motions. The newly discovered stars suggest a disk white dwarf scaleheight larger than the values of 250-350 pc typically assumed in assessments of the local white dwarf density. Both a <V/V_{max}> and a more complex maximum likelihood analysis of the spatial distribution of our likely thin disk white dwarfs yield scaleheights of 400-600 pc while at the same time give a reasonable match to the local white dwarf volume density found in other surveys. Our results could have interesting implications for white dwarfs as potential MACHO objects. We can place some direct constraints (albeit weak ones) on the contribution of halo white dwarfs to the dark matter of the Galaxy. Moreover, the elevated scale height that we measure for the thin disk could alter the interpretation of microlensing results to the extent of making white dwarfs untenable as the dominant MACHO contributor. (Abridged)Comment: 38 pages, 5 figures, to appear in April Ap

Laser printing of silver-based micro-wires in ZrO2 substrate for smart implant applications

Smart implants are endowed with functions of sensing, actuating and control to solve problems that may arise during their use. The assembly of these functions along the implant surface is still a challenge. However, with the advent of 3D printing, it is possible to print on implants’ surface, communication channels or micro-antennas or even sensoric/actuating areas. Hence, a positive impact on the long-term performance of the implants (including hip, dental and knee) may be expected with the proposed approach. Despite titanium and Ti6Al4V titanium alloy are the standard choice for implants fabrication, 3Y-TZP (tetragonal 3% mol yttria-stabilized zirconia) has emerged as a ceramic material suitable to overcome titanium alloy problems, due to its numerous advantages. In this sense, this work is concerned with the ability of printing silver-based communication system in zirconia substrates by using laser technology. For this purpose, micro-cavities were created on ZrO2 substrate, where the silver powder was placed and sintered into them. Through the laser approach, silver-based wires with great quality and low resistivity values were achieved. The flexural strength results showed that the mechanical resistance of zirconia disks was affected by laser micro-wire printing, which decreased as the laser passage was performed. Based on the results, it is believed that the proposed approach seems to be effective for the manufacturing of implants with intrinsic capacities, useful for smart implant applications.This work has been supported by FCT (Fundação para a Ciência e Tecnologia - Portugal) in the scope of the projects UID/EEA/04436/ 2019 and NORTE-01-0145-FEDER-000018-HAMaBICo and Add.Additive_Manufacturing to Portuguese Industry_POCI-01-0247- FEDER-024533. Thank the CNPq (205791/2014-0) and CAPES for the financial support

Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts

We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for "observed" particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg to gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard MS-bar coupling, alpha_s. The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD beta function in the FDH and dimensional reduction schemes.Comment: 44 pages, minor corrections and clarifications include

Measurement of the Strong Coupling alpha s from Four-Jet Observables in e+e- Annihilation

Data from e+e- annihilation into hadrons at centre-of-mass energies between 91 GeV and 209 GeV collected with the OPAL detector at LEP, are used to study the four-jet rate as a function of the Durham algorithm resolution parameter ycut. The four-jet rate is compared to next-to-leading order calculations that include the resummation of large logarithms. The strong coupling measured from the four-jet rate is alphas(Mz0)= 0.1182+-0.0003(stat.)+-0.0015(exp.)+-0.0011(had.)+-0.0012(scale)+-0.0013(mass) in agreement with the world average. Next-to-leading order fits to the D-parameter and thrust minor event-shape observables are also performed for the first time. We find consistent results, but with significantly larger theoretical uncertainties.Comment: 25 pages, 15 figures, Submitted to Euro. Phys. J.