1,471 research outputs found
Remarks on quiver gauge theories from open topological string theory
We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory. This means that we construct the natural A-infinity-structure of open string amplitudes in the associated D-brane category. Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, we prove a general and simple formula for effective superpotentials
Computation of Contour Integrals on
Contour integrals of rational functions over , the moduli
space of -punctured spheres, have recently appeared at the core of the
tree-level S-matrix of massless particles in arbitrary dimensions. The contour
is determined by the critical points of a certain Morse function on . The integrand is a general rational function of the puncture
locations with poles of arbitrary order as two punctures coincide. In this note
we provide an algorithm for the analytic computation of any such integral. The
algorithm uses three ingredients: an operation we call general KLT, Petersen's
theorem applied to the existence of a 2-factor in any 4-regular graph and
Hamiltonian decompositions of certain 4-regular graphs. The procedure is
iterative and reduces the computation of a general integral to that of simple
building blocks. These are integrals which compute double-color-ordered partial
amplitudes in a bi-adjoint cubic scalar theory.Comment: 36+11 p
Connectivity Compression for Irregular Quadrilateral Meshes
Applications that require Internet access to remote 3D datasets are often
limited by the storage costs of 3D models. Several compression methods are
available to address these limits for objects represented by triangle meshes.
Many CAD and VRML models, however, are represented as quadrilateral meshes or
mixed triangle/quadrilateral meshes, and these models may also require
compression. We present an algorithm for encoding the connectivity of such
quadrilateral meshes, and we demonstrate that by preserving and exploiting the
original quad structure, our approach achieves encodings 30 - 80% smaller than
an approach based on randomly splitting quads into triangles. We present both a
code with a proven worst-case cost of 3 bits per vertex (or 2.75 bits per
vertex for meshes without valence-two vertices) and entropy-coding results for
typical meshes ranging from 0.3 to 0.9 bits per vertex, depending on the
regularity of the mesh. Our method may be implemented by a rule for a
particular splitting of quads into triangles and by using the compression and
decompression algorithms introduced in [Rossignac99] and
[Rossignac&Szymczak99]. We also present extensions to the algorithm to compress
meshes with holes and handles and meshes containing triangles and other
polygons as well as quads
Introduction to the AdS/CFT correspondence
This is a pedagogical introduction to the AdS/CFT correspondence, based on
lectures delivered by the author at the third IDPASC school. Starting with the
conceptual basis of the holographic dualities, the subject is developed
emphasizing some concrete topics, which are discussed in detail. A very brief
introduction to string theory is provided, containing the minimal ingredients
to understand the origin of the AdS/CFT duality. Other topics covered are the
holographic calculation of correlation functions, quark-antiquark potentials
and transport coefficients.Comment: 64 pages, 12 figures;v2: minor improvements;v3: references adde
Strings with Discrete Target Space
We investigate the field theory of strings having as a target space an
arbitrary discrete one-dimensional manifold. The existence of the continuum
limit is guaranteed if the target space is a Dynkin diagram of a simply laced
Lie algebra or its affine extension. In this case the theory can be mapped onto
the theory of strings embedded in the infinite discrete line which is the
target space of the SOS model. On the regular lattice this mapping is known as
Coulomb gas picture. ... Once the classical background is known, the amplitudes
involving propagation of strings can be evaluated by perturbative expansion
around the saddle point of the functional integral. For example, the partition
function of the noninteracting closed string (toroidal world sheet) is the
contribution of the gaussian fluctuations of the string field. The vertices in
the corresponding Feynman diagram technique are constructed as the loop
amplitudes in a random matrix model with suitably chosen potential.Comment: 65 pages (Sept. 91
From twistors to twisted geometries
In a previous paper we showed that the phase space of loop quantum gravity on
a fixed graph can be parametrized in terms of twisted geometries, quantities
describing the intrinsic and extrinsic discrete geometry of a cellular
decomposition dual to the graph. Here we unravel the origin of the phase space
from a geometric interpretation of twistors.Comment: 9 page
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