456 research outputs found
Constructive factorization of LPDO in two variables
We study conditions under which a partial differential operator of arbitrary
order in two variables or ordinary linear differential operator admits a
factorization with a first-order factor on the left. The factorization process
consists of solving, recursively, systems of linear equations, subject to
certain differential compatibility conditions. In the generic case of partial
differential operators one does not have to solve a differential equation. In
special degenerate cases, such as ordinary differential, the problem is finally
reduced to the solution of some Riccati equation(s). The conditions of
factorization are given explicitly for second- and, and an outline is given for
the higher-order case.Comment: 16 pages, to be published in Journal "Theor. Math. Phys." (2005
Deforming baryons into confining strings
We find explicit probe D3-brane solutions in the infrared of the
Maldacena-Nunez background. The solutions describe deformed baryon vertices: q
external quarks are separated in spacetime from the remaining N-q. As the
separation is taken to infinity we recover known solutions describing infinite
confining strings in gauge theory. We present results for the
mass of finite confining strings as a function of length. We also find probe
D2-brane solutions in a confining type IIA geometry, the reduction of a G_2
holonomy M theory background. The relation between these deformed baryons and
confining strings is not as straightforward.Comment: 1+13 pages. LaTeX. 3 Figures. Factor of 2N fixed to N for the IIA
background. Minor changes to tex
Non-perturbative gauge superpotentials from supergravity
We study U(N) SQCD with N_f <= N flavors of quarks and antiquarks by
engineering it with a configuration of fractional D3-branes on a C^3 / Z_2 x
Z_2 orbifold. In particular we show how the moduli space of the gauge theory
naturally emerges from the classical geometry produced by the D3-branes, and
how the non-perturbatively generated superpotential is recovered from
geometrical data.Comment: LaTeX, 18 pages, 4 figures; v2: published version with minor changes
and an added referenc
A Detailed Record of Shallow Hydrothermal Fluid Flow in the Sierra Nevada Magmatic Arc from Low-ÎŽ18O Skarn Garnets
Garnet from skarns exposed at Empire Mountain, Sierra Nevada (California, United States) batholith, have variable ÎŽ18O values including the lowest known ÎŽ18O values of skarn garnet (â4.0â°) in North America. Such values indicate that surface-derived meteoric water was a significant component of the fluid budget of the skarn-forming hydrothermal system, which developed in response to shallow emplacement (âŒ3.3 km) of the 109 Ma quartz diorite of Empire Mountain. Values of ÎŽ18O, measured in situ across single garnet crystals by secondary ion mass spectrometry, vary considerably (up to 7â°) and sometimes abruptly, indicating variable mixing of meteoric, magmatic, and metamorphic water. Brecciation in the skarns and alteration of the Empire Mountain pluton suggests that fracture-enhanced permeability was a critical control on the depth to which surface waters penetrated to form skarns and later alter the pluton. Compared to other Sierran systems, much greater volumes of skarn rock suggest an exceptionally vigorous hydrothermal system that saw unusually high levels of decarbonation reaction progress, likely a consequence of the magma intruding relatively cold wallrocks inboard of the main locus of magmatism in the Sierran arc at that time
Non-singlet Baryons in Less Supersymmetric Backgrounds
We analyze the holographic description of non-singlet baryons in various
backgrounds with reduced supersymmetries and/or confinement. We show that they
exist in all AdS_5xY_5 backgrounds with Y_5 an Einstein manifold bearing five
form flux, for a number of quarks 5N/8< k< N, independently on the
supersymmetries preserved. This result still holds for gamma_i deformations. In
the confining Maldacena-Nunez background non-singlet baryons also exist,
although in this case the interval for the number of quarks is reduced as
compared to the conformal case. We generalize these configurations to include a
non-vanishing magnetic flux such that a complementary microscopical description
can be given in terms of lower dimensional branes expanding into fuzzy baryons.
This description is a first step towards exploring the finite 't Hooft coupling
region.Comment: 36 Pages, 1 figure, Latex, v2: few minor changes, JHEP versio
Non-critical supergravity (d>1) and holography
In this paper we investigate the supergravity equations of motion associated
with non-critical () type II string theories that incorporate RR forms.
Using a superpotential formalism we determine several classes of solutions. In
particular we find analytic backgrounds with a structure of and numerical solutions that asymptote a linear dilaton with a
topology of . The SUGRA solutions we have found
can serve as anti holographic descriptions of gauge theories in a large
limit which is different than the one of the critical gauge/gravity duality. It
is characterized by N\rt \infty and . We have made the
first steps in analyzing the corresponding gauge theory properties like Wilson
loops and the glue-ball spectra.Comment: 48 pages, JHEP style, 11 figure
Rotating and Orbiting Strings in the Near-Horizon Brane Backgrounds
Using the Schwarzschild-type coordinates in stead of the global ones we
reconstruct the classical rotating closed string solutions in the AdS*5 x S*5
backgrounds. They are explicitly described by the Jacobi elliptic and
trigonometrical functions of worldsheet coordinates. We study the orbiting
closed string configurations in the near-horizon geometries of Dp, NS1 and NS5
branes, and derive the energy and spin of them, whose relation takes a simple
form for short strings. Specially in the D5 and NS5 backgrounds we have a
linear relation that the energy of the point-like string is proportional to the
spin, which is associated with the spectrum of strings in the pp-wave
geometries obtained by taking a special Penrose limit on the D5 and NS5
backgrounds.Comment: 15 pages, LaTeX, no figure
String Tensions and Three Dimensional Confining Gauge Theories
In the context of gauge/gravity duality, we try to understand better the
proposed duality between the fractional D2-brane supergravity solutions of
(Nucl. Phys. B 606 (2001) 18, hep-th/0101096) and a confining 2+1 dimensional
gauge theory. Based on the similarities between this fractional D2-brane
solution and D3-brane supergravity solutions with more firmly established gauge
theory duals, we conjecture that a confining q-string in the 2+1 dimensional
gauge theory is dual to a wrapped D4-brane. In particular, the D4-brane looks
like a string in the gauge theory directions but wraps a S**3 in S**4 in the
transverse geometry. For one of the supergravity solutions, we find a near
quadratic scaling law for the tension: . Based on the tension,
we conjecture that the gauge theory dual is SU(N) far in the infrared. We also
conjecture that a quadratic or near quadratic scaling is a generic feature of
confining 2+1 dimensional SU(N) gauge theories.Comment: 23 pages, 2 figure
Characterizing Operations Preserving Separability Measures via Linear Preserver Problems
We use classical results from the theory of linear preserver problems to
characterize operators that send the set of pure states with Schmidt rank no
greater than k back into itself, extending known results characterizing
operators that send separable pure states to separable pure states. We also
provide a new proof of an analogous statement in the multipartite setting. We
use these results to develop a bipartite version of a classical result about
the structure of maps that preserve rank-1 operators and then characterize the
isometries for two families of norms that have recently been studied in quantum
information theory. We see in particular that for k at least 2 the operator
norms induced by states with Schmidt rank k are invariant only under local
unitaries, the swap operator and the transpose map. However, in the k = 1 case
there is an additional isometry: the partial transpose map.Comment: 16 pages, typos corrected, references added, proof of Theorem 4.3
simplified and clarifie
A Soluble String Theory of Hadrons
We consider Penrose limits of the Klebanov-Strassler and Maldacena-Nunez
holographic duals to N =1 supersymmetric Yang-Mills. By focusing in on the IR
region we obtain exactly solvable string theory models. These represent the
nonrelativistic motion and low-lying excitations of heavy hadrons with mass
proportional to a large global charge. We argue that these hadrons, both
physically and mathematically, take the form of heavy nonrelativistic strings;
we term them "annulons." A simple toy model of a string boosted along a compact
circle allows us considerable insight into their properties. We also calculate
the Wilson loop carrying large global charge and show the effect of confinement
is quadratic, not linear, in the string tension.Comment: 40 pages, 1 figure; v2: typos correcte
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