77 research outputs found
A language for multiplicative-additive linear logic
A term calculus for the proofs in multiplicative-additive linear logic is
introduced and motivated as a programming language for channel based
concurrency. The term calculus is proved complete for a semantics in linearly
distributive categories with additives. It is also shown that proof equivalence
is decidable by showing that the cut elimination rewrites supply a confluent
rewriting system modulo equations.Comment: 16 pages without appendices, 30 with appendice
N=1 superfield description of vector-tensor couplings in six dimensions
We express supersymmetric couplings among the vector and the tensor
multiplets in six dimensions (6D) in terms of N=1 superfields. The superfield
description is derived from the invariant action in the projective superspace.
The obtained expression is consistent with the known superfield actions of 6D
supersymmetric gauge theory and 5D Chern-Simons theory after the dimensional
reduction. Our result provides a crutial clue to the N=1 superfield description
of 6D supergravity.Comment: 28 pages, v2:a reference adde
A magic pyramid of supergravities
By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and
single set of transformation rules, but with fields valued respectively in
R,C,H,O, it was recently shown that tensoring left and right multiplets yields
a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was
subsequently tied in with the more familiar R,C,H,O description of spacetime to
give a unified division-algebraic description of extended super Yang-Mills in D
= 3, 4, 6, 10. Here, these constructions are brought together resulting in a
magic pyramid of supergravities. The base of the pyramid in D = 3 is the known
4x4 magic square, while the higher levels are comprised of a 3x3 square in D =
4, a 2x2 square in D = 6 and Type II supergravity at the apex in D = 10. The
corresponding U-duality groups are given by a new algebraic structure, the
magic pyramid formula, which may be regarded as being defined over three
division algebras, one for spacetime and each of the left/right Yang-Mills
multiplets. We also construct a conformal magic pyramid by tensoring conformal
supermultiplets in D = 3, 4, 6. The missing entry in D = 10 is suggestive of an
exotic theory with G/H duality structure F4(4)/Sp(3) x Sp(1).Comment: 30 pages, 6 figures. Updated to match published version. References
and comments adde
Partially twisted superconformal M5 brane in R-symmetry gauge field backgrounds
We obtain the action for a curved superconformal abelian M5 brane with the
background R-symmetry gauge field turned on. We then restrict ourselves to
superconformal M5 brane on a sphere times flat Minkowski space. We choose
R-symmetry SO(1,4) instead of SO(5), which enables us to partially twist on
Minkowski space and replace it by some curved Lorentzian manifold. We obtain M5
brane actions on and where actions
and all fields, including the background gauge field, are real. Dimensional
reduction along time gives real 5d SYM actions with nonabelian generalizations.Comment: 31 pages, a discussion on unitarity is adde
Towards an M5-Brane Model I: A 6d Superconformal Field Theory
We present an action for a six-dimensional superconformal field theory
containing a non-abelian tensor multiplet. All of the ingredients of this
action have been available in the literature. We bring these pieces together by
choosing the string Lie 2-algebra as a gauge structure, which we motivated in
previous work. The kinematical data contains a connection on a categorified
principal bundle, which is the appropriate mathematical description of the
parallel transport of self-dual strings. Our action can be written down for
each of the simply laced Dynkin diagrams, and each case reduces to a
four-dimensional supersymmetric Yang--Mills theory with corresponding gauge Lie
algebra. Our action also reduces nicely to an M2-brane model which is a
deformation of the ABJM model. While this action is certainly not the desired
M5-brane model, we regard it as a key stepping stone towards a potential
construction of the (2,0)-theory.Comment: 1+39 pages, v3: minor improvements, published versio
On curvature squared terms in N = 2 supergravity
We present the N = 2 supersymmetric completion of a scalar curvature squared
term in a completely gauge independent form. We also elaborate on its component
structure.Comment: 15 pages; V2: 17 pages, typos corrected, discussion comments and
acknowledgement added; V3: published versio
A Tensor Library for Scientific Computing
The majority of physical phenomena and their computational simulations are described mathematically in terms of tensors and their different algebraic operations. Possibly the most used tensors are the ones of rank 1 and 2, which correspond to the algebraic concepts of vectors and matrices, respectively. Nevertheless, higher rank tensors (specially 3 and 4) appear at all times in different branches of physics and in numerical methods. One of the major drawbacks of high
performance computing is that the code necessary to perform such tensor operations looks different and it is several lines longer than the corresponding one-line mathematical representation. Here we present a C++ tensor library, called LTensor, that we have developed using modern concepts of
object oriented design and expression templates. As it will be shown, the LTensor library is able to mimic the classical indicial notation and follows Einstein convention about indices. Furthermore, it has other additional features than distinguish it from other libraries based on similar concepts: dynamic dimension size, arbitrary contraction order, customizable storage, inherited class structure, arbitrary looping positions on indicial notations, etc.Fil: Limache, Alejandro Cesar. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria QuÃmica. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria QuÃmica; ArgentinaFil: Rojas Fredini, Pablo Sebastián. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria QuÃmica. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria QuÃmica; Argentin
Supersymmetric Brane World Scenarios from Off-Shell Supergravity
Using N=2 off-shell supergravity in five dimensions, we supersymmetrize the
brane world scenario of Randall and Sundrum. We extend their construction to
include supersymmetric matter at the fixpoints.Comment: 15 pages, no figures, late
Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of
gravity where an arbitrary function of the GB invariant, , is added to
the General Relativity action. We show that such theory is endowed with a quite
rich cosmological structure: it may naturally lead to an effective cosmological
constant, quintessence or phantom cosmic acceleration, with a possible
transition from deceleration to acceleration. It is demonstrated in the paper
that this theory is perfectly viable, since it is compliant with Solar System
constraints. Specific properties of gravity in a de Sitter universe,
such as dS and SdS solutions, their entropy and its explicit one-loop
quantization are studied. The issue of a possible solution of the hierarchy
problem in modified gravities is addressed too.Comment: LaTeX file 20 pages, new subsections are adde
- …