14,556 research outputs found
Bound-state gravity from higher derivatives
In certain Lorentz-covariant higher-derivative field theories of spins < or
=1, would-be ultraviolet divergences generate color-singlet poles as infrared
divergences. Absence of higher-order poles implies ten-dimensional
supersymmetric Yang-Mills with bound-state supergravity, in close analogy with
open string theory.Comment: TeX file, 12 pages, 4 figure
Entropy-based convergence rates of greedy algorithms
We present convergence estimates of two types of greedy algorithms in terms
of the metric entropy of underlying compact sets. In the first part, we measure
the error of a standard greedy reduced basis method for parametric PDEs by the
metric entropy of the solution manifold in Banach spaces. This contrasts with
the classical analysis based on the Kolmogorov n-widths and enables us to
obtain direct comparisons between the greedy algorithm error and the entropy
numbers, where the multiplicative constants are explicit and simple. The
entropy-based convergence estimate is sharp and improves upon the classical
width-based analysis of reduced basis methods for elliptic model problems. In
the second part, we derive a novel and simple convergence analysis of the
classical orthogonal greedy algorithm for nonlinear dictionary approximation
using the metric entropy of the symmetric convex hull of the dictionary. This
also improves upon existing results by giving a direct comparison between the
algorithm error and the metric entropy.Comment: 22 pages, no figure
Left-handed string and CHY amplitude at one loop
We propose a generalized left-handed (chiral) gauge choice for the genus one
Riemann surface, realized through a singular gauge transformation of worldsheet
coordinates. The transformation predominantly affects the logarithmic non-zero
modes of the Green's function, leaving non-holomorphic and non-logarithmic
modes unchanged. This procedure yields -functions for chiral
coordinates and box-diagram-like integrals in terms of modular parameters. The
resulting -functions formulate one-loop level Scattering Equations that
simplify to satisfy the tree-level solutions, constraining the locations of the
marked points. Subsequent integrals agree with the field-theoretic box diagram
for the four-point amplitude, in accordance with the divergent
expansions derived from dimensional regularization in the infrared limit. We
conclude by highlighting potential avenues for future research, including the
exploration of methodologies that preclude the need for worldsheet coordinates
reparametrization and their implications for accurately capturing infrared
behavior from modular parameter integrals
Loop Variables and Gauge Invariant Exact Renormalization Group Equations for (Open) String Theory
An exact renormalization group equation is written down for the world sheet
theory describing the bosonic open string in general backgrounds. Loop variable
techniques are used to make the equation gauge invariant. This is worked out
explicitly up to level 3. The equation is quadratic in the fields and can be
viewed as a proposal for a string field theory equation. As in the earlier loop
variable approach, the theory has one extra space dimension and mass is
obtained by dimensional reduction. Being based on the sigma model RG, it is
background independent.
It is intriguing that in contrast to BRST string field theory, the gauge
transformations are not modified by the interactions up to the level
calculated. The interactions can be written in terms of gauge invariant field
strengths for the massive higher spin fields and the non zero mass is essential
for this. This is reminiscent of Abelian Born-Infeld action (along with
derivative corrections) for the massless vector field, which is also written in
terms of the field strength.Comment: Latex file, 40 pages.Some typos corrected and cosmetic change
Pion Transparency in 500 MeV C(pi,pi') Reactions?
The question whether there is a pion transparency in 500 MeV scatterings is studied using a semiclassical, hadronic transport
model. The double differential cross sections of this reaction measured at
LAMPF can be largely accounted for, if one uses energy-dependent, anisotropic
angular distributions which are fitted to pion-nucleon scattering data for the
decay of and resonances. The remaining discrepancy
between the data and the calculation sets a limit on effects of more exotic
processes.Comment: Latex file, 11 pages, 3 figures availabe upon request. Phys. Lett. B
in pres
Tool for Viewing Faults Under Terrain
Multi Surface Light Table (MSLT) is an interactive software tool that was developed in support of the QuakeSim project, which has created an earthquake- fault database and a set of earthquake- simulation software tools. MSLT visualizes the three-dimensional geometries of faults embedded below the terrain and animates time-varying simulations of stress and slip. The fault segments, represented as rectangular surfaces at dip angles, are organized into collections, that is, faults. An interface built into MSLT queries and retrieves fault definitions from the QuakeSim fault database. MSLT also reads time-varying output from one of the QuakeSim simulation tools, called "Virtual California." Stress intensity is represented by variations in color. Slips are represented by directional indicators on the fault segments. The magnitudes of the slips are represented by the duration of the directional indicators in time. The interactive controls in MSLT provide a virtual track-ball, pan and zoom, translucency adjustment, simulation playback, and simulation movie capture. In addition, geographical information on the fault segments and faults is displayed on text windows. Because of the extensive viewing controls, faults can be seen in relation to one another, and to the terrain. These relations can be realized in simulations. Correlated slips in parallel faults are visible in the playback of Virtual California simulations
Tamagawa Products for Elliptic Curves Over Number Fields
In recent work, Griffin, Ono, and Tsai constructs an series to prove that
the proportion of short Weierstrass elliptic curves over with
trivial Tamagawa product is and that the average Tamagawa product
is . Following their work, we generalize their series over
arbitrary number fields to be where
is the proportion of short Weierstrass elliptic curves
over with Tamagawa product . We then construct Markov chains to compute
the exact values of for all number fields and
positive integers . As a corollary, we also compute the average Tamagawa
product . We then use these results to uniformly bound
and in terms of the degree of
. Finally, we show that there exist sequences of for which
tends to and to ,
as well as sequences of for which and
tend to .Comment: 40 pages, 9 figures, 17 table
Field Theoretic Study of Bilayer Membrane Fusion III: Membranes with Leaves of Different Composition
We extend previous work on homogeneous bilayers to calculate the barriers to
fusion of planar bilayers which contain two different amphiphiles, a
lamellae-former and a hexagonal former, with different compositions of the
twoin each leaf. Self-consistent field theory is employed, and both standard
and alternative pathways are explored. We first calculate these barriers as the
amount of hexagonal former is increased equally in both leaves to levels
appropriate to the plasma membrane of human red blood cells. We follow these
barriers as the composition of hexagonal-formers is then increased in the cis
layer and decreased in the trans layer, again to an extent comparable to the
biological system. We find that, while the fusion pathway exhibits two barriers
in both the standard and alternative pathways, in both cases the magnitudes of
these barriers are comparable to one another, and small, on the order of 13 kT.
As a consequence, one expects that once the bilayers are brought sufficiently
close to one another to initiate the process, fusion should occur rapidly.Comment: 9 figure
Who changes the string coupling ?
In general bosonic closed string backgrounds the ghost-dilaton is not the
only state in the semi-relative BRST cohomology that can change the
dimensionless string coupling. This fact is used to establish complete dilaton
theorems in closed string field theory. The ghost-dilaton, however, is the
crucial state: for backgrounds where it becomes BRST trivial we prove that the
string coupling becomes an unobservable parameter of the string action. For
backgrounds where the matter CFT includes free uncompactified bosons we
introduce a refined BRST problem by including the zero-modes "x" of the bosons
as legal operators on the complex. We argue that string field theory can be
defined on this enlarged complex and that its BRST cohomology captures
accurately the notion of a string background. In this complex the ghost-dilaton
appears to be the only BRST-physical state changing the string coupling.Comment: 34 pages, phyzz
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