708 research outputs found
HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants
Hilbert scheme topological invariants of plane curve singularities are
identified to framed threefold stable pair invariants. As a result, the
conjecture of Oblomkov and Shende on HOMFLY polynomials of links of plane curve
singularities is given a Calabi-Yau threefold interpretation. The motivic
Donaldson-Thomas theory developed by M. Kontsevich and the third author then
yields natural motivic invariants for algebraic knots. This construction is
motivated by previous work of V. Shende, C. Vafa and the first author on the
large duality derivation of the above conjecture.Comment: 59 pages; v2 references added, minor corrections; v3: exposition
improved, proofs expanded, results unchanged, to appear in Comm. Num. Th.
Phy
Freed-Witten anomaly in general flux compactification
Turning on a NS-NS three-form flux in a compact space drives some D-branes to
be either Freed-Witten anomalous or unstable to decay into fluxes by the
appearance of instantonic branes. By applying T-duality on a toroidal
compactification, the NS-flux is transformed into metric fluxes. We propose a
T-dual version of the Atiyah-Hirzebruch Spectral Sequence upon which we
describe the Freed-Witten anomaly and the brane-flux transition driven by NS
and metric fluxes in a twisted torus. The required conditions to cancel the
anomaly and the appearance of new instantonic branes are also described. In
addition, we give an example in which all D6-branes wrapping Freed-Witten
anomaly-free three-cycles in the twisted torus T^6/Z(2)XZ(2) are nevertheless
unstable to be transformed into fluxes. Evenmore we find a topological
transformation between RR, NS-NS and metric fluxes driven by a chain of
instantonic branes.Comment: v3: Shortened version. Examples added. Main results unchange
A Compiler and Runtime Infrastructure for Automatic Program Distribution
This paper presents the design and the implementation of a compiler and runtime infrastructure for automatic program distribution. We are building a research infrastructure that enables experimentation with various program partitioning and mapping strategies and the study of automatic distribution's effect on resource consumption (e.g., CPU, memory, communication). Since many optimization techniques are faced with conflicting optimization targets (e.g., memory and communication), we believe that it is important to be able to study their interaction.
We present a set of techniques that enable flexible resource modeling and program distribution. These are: dependence analysis, weighted graph partitioning, code and communication generation, and profiling. We have developed these ideas in the context of the Java language. We present in detail the design and implementation of each of the techniques as part of our compiler and runtime infrastructure. Then, we evaluate our design and present preliminary experimental data for each component, as well as for the entire system
Quantization of the Chern-Simons Coupling Constant
We investigate the quantum consistency of p-form Maxwell-Chern-Simons
electrodynamics in 3p+2 spacetime dimensions (for p odd). These are the
dimensions where the Chern--Simons term is cubic, i.e., of the form FFA. For
the theory to be consistent at the quantum level in the presence of magnetic
and electric sources, we find that the Chern--Simons coupling constant must be
quantized. We compare our results with the bosonic sector of eleven dimensional
supergravity and find that the Chern--Simons coupling constant in that case
takes its corresponding minimal allowed value.Comment: 15 pages, 1 figure, JHEP3.cls. Equation (8.6) corrected and perfect
agreement with previous results is obtaine
Duality symmetry and the form fields of M-theory
In previous work we derived the topological terms in the M-theory action in
terms of certain characters that we defined. In this paper, we propose the
extention of these characters to include the dual fields. The unified treatment
of the M-theory four-form field strength and its dual leads to several
observations. In particular we elaborate on the possibility of a twisted
cohomology theory with a twist given by degrees greater than three.Comment: 12 pages, modified material on the differentia
User-Defined Data Distributions in High-Level Programming Languages
One of the characteristic features of todayâs high performance
computing systems is a physically distributed
memory. Efficient management of locality is essential
for meeting key performance requirements for these architectures.
The standard technique for dealing with
this issue has involved the extension of traditional sequential
programming languages with explicit message passing,
in the context of a processor-centric view of
parallel computation. This has resulted in complex and
error-prone assembly-style codes in which algorithms
and communication are inextricably interwoven.
This paper presents a high-level approach to the design
and implementation of data distributions. Our
work is motivated by the need to improve the current
parallel programming methodology by introducing
a paradigm supporting the development of efficient and
reusable parallel code. This approach is currently being
implemented in the context of a new programming
language called Chapel, which is designed in the HPCS
project Cascade
11D supergravity at
We compute certain spinorial cohomology groups controlling possible
supersymmetric deformations of eleven-dimensional supergravity up to order
in the Planck length. At and the spinorial
cohomology groups are trivial and therefore the theory cannot be deformed
supersymmetrically. At the corresponding spinorial cohomology
group is generated by a nontrivial element. On an eleven-dimensional manifold
such that , this element corresponds to a supersymmetric
deformation of the theory, which can only be redefined away at the cost of
shifting the quantization condition of the four-form field strength.Comment: 10 pages, 1 figure. v2: references adde
M-theory and Characteristic Classes
In this note we show that the Chern-Simons and the one-loop terms in the
M-theory action can be written in terms of new characters involving the
M-theory four-form and the string classes. This sheds a new light on the
topological structure behind M-theory and suggests the construction of a theory
of `higher' characteristic classes.Comment: 8 pages. Error in gravitational term fixed; minor corrections;
reference and acknowledgement adde
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