44,213 research outputs found
Cosmological intersecting brane solutions
The recent discovery of an explicit dynamical description of p-branes makes
it possible to investigate the existence of intersection of such objects. We
generalize the solutions depending on the overall transverse space coordinates
and time to those which depend also on the relative transverse space and
satisfy new intersection rules. We give classification of these dynamical
intersecting brane solutions involving two branes, and discuss the application
of these solutions to cosmology and show that these give
Friedmann-Lemaitre-Robertson-Walker cosmological solutions. Finally, we
construct the brane world models, using the (cut-)copy-paste method after
compactifying the trivial spatial dimensions. We then find that interesting
brane world models can be obtained from codimension-one branes and several
static branes with higher codimensions. We also classify the behaviors of the
brane world near the future/past singularity.Comment: 47 pages, 1 figure; v3: minor corrections, references adde
Loop operators and S-duality from curves on Riemann surfaces
We study Wilson-'t Hooft loop operators in a class of N=2 superconformal
field theories recently introduced by Gaiotto. In the case that the gauge group
is a product of SU(2) groups, we classify all possible loop operators in terms
of their electric and magnetic charges subject to the Dirac quantization
condition. We then show that this precisely matches Dehn's classification of
homotopy classes of non-self-intersecting curves on an associated Riemann
surface--the same surface which characterizes the gauge theory. Our analysis
provides an explicit prediction for the action of S-duality on loop operators
in these theories which we check against the known duality transformation in
several examples.Comment: 41 page
Planes, branes and automorphisms: I. Static branes
This is the first of a series of papers devoted to the group-theoretical
analysis of the conditions which must be satisfied for a configuration of
intersecting M5-branes to be supersymmetric. In this paper we treat the case of
static branes. We start by associating (a maximal torus of) a different
subgroup of Spin(10) with each of the equivalence classes of supersymmetric
configurations of two M5-branes at angles found by Ohta & Townsend. We then
consider configurations of more than two intersecting branes. Such a
configuration will be supersymmetric if and only if the branes are G-related,
where G is a subgroup of Spin(10) contained in the isotropy of a spinor. For
each such group we determine (a lower bound for) the fraction of the
supersymmetry which is preserved. We give examples of configurations consisting
of an arbitrary number of non-coincident intersecting fivebranes with
fractions: 1/32, 1/16, 3/32, 1/8, 5/32, 3/16 and 1/4, and we determine the
resulting (calibrated) geometry.Comment: 26 pages (Added a reference and modified one table slightly.
Classification of p-branes, NUTs, Waves and Intersections
We give a full classification of the multi-charge supersymmetric -brane
solutions in the massless and massive maximal supergravities in dimensions
obtained from the toroidal reduction of eleven-dimensional
supergravity. We derive simple universal rules for determining the fractions of
supersymmetry that they preserve. By reversing the steps of dimensional
reduction, the -brane solutions become intersections of -branes, NUTs and
waves in D=10 or D=11. Having classified the lower-dimensional -branes, this
provides a classification of all the intersections in D=10 and D=11 where the
harmonic functions depend on the space transverse to all the individual
objects. We also discuss the structure of U-duality multiplets of -brane
solutions, and show how these translate into multiplets of harmonic and
non-harmonic intersections.Comment: Latex, 67 pages, minor correction
Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification
We present an efficient method for classifying the morphology of the
intersection curve of two quadrics (QSIC) in PR3, 3D real projective space;
here, the term morphology is used in a broad sense to mean the shape,
topological, and algebraic properties of a QSIC, including singularity,
reducibility, the number of connected components, and the degree of each
irreducible component, etc. There are in total 35 different QSIC morphologies
with non-degenerate quadric pencils. For each of these 35 QSIC morphologies,
through a detailed study of the eigenvalue curve and the index function jump we
establish a characterizing algebraic condition expressed in terms of the Segre
characteristics and the signature sequence of a quadric pencil. We show how to
compute a signature sequence with rational arithmetic so as to determine the
morphology of the intersection curve of any two given quadrics. Two immediate
applications of our results are the robust topological classification of QSIC
in computing B-rep surface representation in solid modeling and the derivation
of algebraic conditions for collision detection of quadric primitives
Dynamics of intersecting brane systems -- Classification and their applications --
We present dynamical intersecting brane solutions in higher-dimensional
gravitational theory coupled to dilaton and several forms. Assuming the forms
of metric, form fields, and dilaton field, we give a complete classification of
dynamical intersecting brane solutions with/without M-waves and Kaluza-Klein
monopoles in eleven-dimensional supergravity. We apply these solutions to
cosmology and black holes. It is shown that these give FRW cosmological
solutions and in some cases Lorentz invariance is broken in our world. If we
regard the bulk space as our universe, we may interpret them as black holes in
the expanding universe. We also discuss lower-dimensional effective theories
and point out naive effective theories may give us some solutions which are
inconsistent with the higher-dimensional Einstein equations.Comment: 44 pages; v2: minor corrections, references adde
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