909 research outputs found
Conformal coupling of the scalar field with gravity in higher dimensions and invariant powers of the Laplacian
The hierarchy of conformally coupled scalars with the increasing scaling
dimensions , connected with the -th Euler
density in the corresponding space-time dimensions is proposed. The
corresponding conformal invariant Lagrangian with the -th power of Laplacian
for the already known cases is reviewed, and the subsequent case of
is completely constructed and analyzed.Comment: Latex, 11 pages, v.2, two misprints correcte
Axial anomaly with the overlap-Dirac operator in arbitrary dimensions
We evaluate for arbitrary even dimensions the classical continuum limit of
the lattice axial anomaly defined by the overlap-Dirac operator. Our
calculational scheme is simple and systematic. In particular, a powerful
topological argument is utilized to determine the value of a lattice integral
involved in the calculation. When the Dirac operator is free of species
doubling, the classical continuum limit of the axial anomaly in various
dimensions is combined into a form of the Chern character, as expected.Comment: 9 pages, uses JHEP.cls and amsfonts.sty, the final version to appear
in JHE
A New Anomaly Matching Condition?
We formulate ``Witten'' matching conditions for confining gauge theories. The
conditions are analogous to 't Hooft's, but involve Witten's global SU(2)
anomaly. Using a group theoretic result of Geng, Marshak, Zhao and Okubo, we
show that if the fourth homotopy group of the flavor group is trivial
() then realizations of massless composite fermions that satisfy
the 't Hooft conditions also satisfy the Witten conditions. If is
nontrivial, the new matching conditions can yield additional information about
the low energy spectrum of the theory. We give a simple physical proof of Geng,
et. al.'s result.Comment: 11 pages, LaTex, all macros include
Bound state spectra of three-body muonic molecular ions
The results of highly accurate calculations are presented for all twenty-two
known bound and states in the six
three-body muonic molecular ions and
. A number of bound state properties of these muonic molecular ions have
been determined numerically to high accuracy. The dependence of the total
energies of these muonic molecules upon particle masses is considered. We also
discuss the current status of muon-catalysis of nuclear fusion reactions.Comment: This is the final version. All `techical' troubles with the
Latex-file have been resolved. A few misprints/mistakes in the text were
correcte
Boron doped TiO2 catalysts for photocatalytic ozonation of aqueous mixtures of common pesticides: Diuron, o-phenylphenol, MCPA and terbuthylazine
Photocatalysts were characterized by ICP-EOS, N2 adsorption-desorption, XRD, XPS, and DR-UV-Vis spectroscopy. Four recalcitrant herbicides and pesticides (diuron, o-phenylphenol, 2-methyl-4-chlorophenoxyacetic acid (MCPA) and terbuthylazine) were subjected to degradation by ozonation, photolytic ozonation, photocatalysis and photocatalytic ozonation using the prepared catalysts under simulated solar irradiation in a laboratory scale system. The boron that was not incorporated to the TiO2 interstitial positions was unstable and leached to the solution. The washed B-doped TiO2 catalysts, with 0.5-0.8 wt.% of interstitial boron were more active than bare TiO2 for the removal and mineralization of the target compounds. The combination of ozonation and photocatalysis led to faster mineralization rates and allowed the complete removal of the pesticides below the regulatory standards. The B-doped catalyst was stable and maintained 75% mineralization after 3 consecutive runs
On a coordinate independent description of string worldsheet theory
We study worldsheet conformal invariance for bosonic string propagating in a
curved background using the hamiltonian formalism. In order to formulate the
problem in a background independent manner we first rewrite the worldsheet
theory in a language where it describes a single particle moving in an
infinite-dimensional curved spacetime. This language is developed at a formal
level without regularizing the infinite-dimensional traces. Then we adopt
DeWitt's (Phys.Rev.85:653-661,1952) coordinate independent formulation of
quantum mechanics in the present context. Given the expressions for the
classical Virasoro generators, this procedure enables us to define the
coordinate invariant quantum analogues which we call DeWitt-Virasoro
generators. This framework also enables us to calculate the invariant matrix
elements of an arbitrary operator constructed out of the DeWitt-Virasoro
generators between two arbitrary scalar states. Using these tools we further
calculate the DeWitt-Virasoro algebra in spin-zero representation. The result
is given by the Witt algebra with additional anomalous terms that vanish for
Ricci-flat backgrounds. Further analysis need to be performed in order to
precisely relate this with the beta function computation of Friedan and others.
Finally, we explain how this analysis improves the understanding of showing
conformal invariance for certain pp-wave that has been recently discussed using
hamiltonian framework.Comment: 32 pages, some reorganization for more elaborate explanation, no
change in conclusio
Two-Loop Superstrings IV, The Cosmological Constant and Modular Forms
The slice-independent gauge-fixed superstring chiral measure in genus 2
derived in the earlier papers of this series for each spin structure is
evaluated explicitly in terms of theta-constants. The slice-independence allows
an arbitrary choice of superghost insertion points q_1, q_2 in the explicit
evaluation, and the most effective one turns out to be the split gauge defined
by S_{\delta}(q_1,q_2)=0. This results in expressions involving bilinear
theta-constants M. The final formula in terms of only theta-constants follows
from new identities between M and theta-constants which may be interesting in
their own right. The action of the modular group Sp(4,Z) is worked out
explicitly for the contribution of each spin structure to the superstring
chiral measure. It is found that there is a unique choice of relative phases
which insures the modular invariance of the full chiral superstring measure,
and hence a unique way of implementing the GSO projection for even spin
structure. The resulting cosmological constant vanishes, not by a Riemann
identity, but rather by the genus 2 identity expressing any modular form of
weight 8 as the square of a modular form of weight 4. The degeneration limits
for the contribution of each spin structure are determined, and the
divergences, before the GSO projection, are found to be the ones expected on
physical grounds.Comment: 58 pages, no figure
A Theory of a Spot
We present a simple inflationary scenario that can produce arbitrarily large
spherical underdense or overdense regions embedded in a standard Lambda cold
dark matter paradigm, which we refer to as bubbles. We analyze the effect such
bubbles would have on the Cosmic Microwave Background (CMB). For super-horizon
sized bubble in the vicinity of the last scattering surface, a signal is
imprinted onto CMB via a combination of Sach-Wolfe and an early integrated
Sach-Wolfe (ISW) effects. Smaller, sub-horizon sized bubbles at lower redshifts
(during matter domination and later) can imprint secondary anisotropies on the
CMB via Rees-Sciama, late-time ISW and Ostriker-Vishniac effects. Our scenario,
and arguably most similar inflationary models, produce bubbles which are
over/underdense in potential: in density such bubbles are characterized by
having a distinct wall with the interior staying at the cosmic mean density. We
show that such models can potentially, with only moderate fine tuning, explain
the \emph{cold spot}, a non-Gaussian feature identified in the Wilkinson
Microwave Anisotropy Probe (WMAP) data by several authors. However, more
detailed comparisons with current and future CMB data are necessary to confirm
(or rule out) this scenario.Comment: 19 pages, 19 figures, added references and explanations, JCAP in
pres
Two-Loop Superstrings II, The Chiral Measure on Moduli Space
A detailed derivation from first principles is given for the unambiguous and
slice-independent formula for the two-loop superstring chiral measure which was
announced in the first paper of this series. Supergeometries are projected onto
their super period matrices, and the integration over odd supermoduli is
performed by integrating over the fibers of this projection. The subtleties
associated with this procedure are identified. They require the inclusion of
some new finite-dimensional Jacobian superdeterminants, a deformation of the
worldsheet correlation functions using the stress tensor, and perhaps
paradoxically, another additional gauge choice, ``slice \hat\mu choice'', whose
independence also has to be established. This is done using an important
correspondence between superholomorphic notions with respect to a supergeometry
and holomorphic notions with respect to its super period matrix. Altogether,
the subtleties produce precisely the corrective terms which restore the
independence of the resulting gauge-fixed formula under infinitesimal changes
of gauge-slice. This independence is a key criterion for any gauge-fixed
formula and hence is verified in detail.Comment: 64 pages, no figure
Two-Loop Superstrings V: Gauge Slice Independence of the N-Point Function
A systematic construction of superstring scattering amplitudes for
massless NS bosons to two loop order is given, based on the projection of
supermoduli space onto super period matrices used earlier for the superstring
measure in the first four papers of this series. The one important new
difficulty arising for the -point amplitudes is the fact that the projection
onto super period matrices introduces corrections to the chiral vertex
operators for massless NS bosons which are not pure (1,0) differential forms.
However, it is proved that the chiral amplitudes are closed differential forms,
and transform by exact differentials on the worldsheet under changes of gauge
slices. Holomorphic amplitudes and independence of left from right movers are
recaptured after the extraction of terms which are Dolbeault exact in one
insertion point, and de Rham closed in the remaining points. This allows a
construction of GSO projected, integrated superstring scattering amplitudes
which are independent of the choice of gauge slices and have only physical
kinematical singularities.Comment: 33 pages, no figur
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