21,907 research outputs found
Fermionic one-loop amplitudes of the RNS superstring
We investigate massless n-point one-loop amplitudes of the open RNS
superstring with two external fermions and determine their worldsheet
integrands. The contributing correlation functions involving spin-1/2 and
spin-3/2 operators from the fermion vertices are evaluated to any multiplicity.
Moreover, we introduce techniques to sum these correlators over the spin
structures of the worldsheet fermions such as to manifest all cancellations due
to spacetime supersymmetry. These spin sums require generalizations of the
Riemann identities among Jacobi theta functions, and the results can be
expressed in terms of doubly-periodic functions known from the mathematics
literature on elliptic multiple zeta values. On the boundary of moduli space,
our spin-summed correlators specialize to compact representations of fermionic
one-loop integrands for ambitwistor strings.Comment: 42+24 pages, v2: published version, minor corrections in (4.5), (4.8)
and (4.15
Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix
The positive semidefinite rank of a nonnegative -matrix~ is
the minimum number~ such that there exist positive semidefinite -matrices , such that S(k,\ell) =
\mbox{tr}(A_k^* B_\ell).
The most important, lower bound technique for nonnegative rank is solely
based on the support of the matrix S, i.e., its zero/non-zero pattern. In this
paper, we characterize the power of lower bounds on positive semidefinite rank
based on solely on the support.Comment: 9 page
Constructing Reference Metrics on Multicube Representations of Arbitrary Manifolds
Reference metrics are used to define the differential structure on multicube
representations of manifolds, i.e., they provide a simple and practical way to
define what it means globally for tensor fields and their derivatives to be
continuous. This paper introduces a general procedure for constructing
reference metrics automatically on multicube representations of manifolds with
arbitrary topologies. The method is tested here by constructing reference
metrics for compact, orientable two-dimensional manifolds with genera between
zero and five. These metrics are shown to satisfy the Gauss-Bonnet identity
numerically to the level of truncation error (which converges toward zero as
the numerical resolution is increased). These reference metrics can be made
smoother and more uniform by evolving them with Ricci flow. This smoothing
procedure is tested on the two-dimensional reference metrics constructed here.
These smoothing evolutions (using volume-normalized Ricci flow with DeTurck
gauge fixing) are all shown to produce reference metrics with constant scalar
curvatures (at the level of numerical truncation error).Comment: 37 pages, 16 figures; additional introductory material added in
version accepted for publicatio
The Anisotropic Two-Point Correlation Functions of the Nonlinear Traceless Tidal Field in the Principal-Axis Frame
Galaxies on the largest scales of the Universe are observed to be embedded in
the filamentary cosmic web which is shaped by the nonlinear tidal field. As an
efficient tool to quantitatively describe the statistics of this cosmic web, we
present the anisotropic two-point correlation functions of the nonlinear
traceless tidal field in the principal-axis frame, which are measured using
numerical data from an N-body simulation. We show that both of the nonlinear
density and traceless tidal fields are more strongly correlated along the
directions perpendicular to the eigenvectors associated with the largest
eigenvalues of the local tidal field. The correlation length scale of the
traceless tidal field is found to be ~20 Mpc/h, which is much larger than that
of the density field ~5 Mpc/h. We also provide analytic fitting formulae for
the anisotropic correlation functions of the traceless tidal field, which turn
out to be in excellent agreement with the numerical results. We expect that our
numerical results and analytic formula are useful to disentangle cosmological
information from the filamentary network of the large-scale structures.Comment: ApJ in press, accepted version, minor changes, discussion improve
Fooling sets and rank
An matrix is called a \textit{fooling-set matrix of size }
if its diagonal entries are nonzero and for every
. Dietzfelbinger, Hromkovi{\v{c}}, and Schnitger (1996) showed that
n \le (\mbox{rk} M)^2, regardless of over which field the rank is computed,
and asked whether the exponent on \mbox{rk} M can be improved.
We settle this question. In characteristic zero, we construct an infinite
family of rational fooling-set matrices with size n = \binom{\mbox{rk}
M+1}{2}. In nonzero characteristic, we construct an infinite family of
matrices with n= (1+o(1))(\mbox{rk} M)^2.Comment: 10 pages. Now resolves the open problem also in characteristic
Petty Officer Lee Oliver, interviewed by Shavonne Brosnan
Petty Officer Lee Oliver, interviewed by Shavonne Brosnan, June 1, 2003. Text: 15 pp. transcript. Time: 00:29:57.
Listen:
mfc_na3248_c2361_01Ahttps://digitalcommons.library.umaine.edu/mf144/1071/thumbnail.jp
Gauge drivers for the generalized harmonic Einstein equations
The generalized harmonic representation of Einstein's equations is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity community are incompatible with the hyperbolicity of the equations in this form. This paper presents a new method of imposing gauge conditions that preserves hyperbolicity for a much wider class of conditions, including as special cases many of the standard ones used in numerical relativity: e.g., K freezing, Gamma freezing, Bona-Massó slicing, conformal Gamma drivers, etc. Analytical and numerical results are presented which test the stability and the effectiveness of this new gauge-driver evolution system
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