281,537 research outputs found
Schwinger-Dyson and Large Loop Equation for Supersymmetric Yang-Mills Theory
We derive an infinite sequence of Schwinger-Dyson equations for
supersymmetric Yang-Mills theory. The fundamental and the only variable
employed is the Wilson-loop geometrically represented in superspace: it
organizes an infinite number of supersymmetrizing insertions into the ordinary
Wilson-loop as a single entity. In the large limit, our equation
becomes a closed loop equation for the one-point function of the Wilson-loop
average.Comment: 9 pages, Late
Diagram spaces, diagram spectra, and spectra of units
This article compares the infinite loop spaces associated to symmetric
spectra, orthogonal spectra, and EKMM S-modules. Each of these categories of
structured spectra has a corresponding category of structured spaces that
receives the infinite loop space functor \Omega^\infty. We prove that these
models for spaces are Quillen equivalent and that the infinite loop space
functors \Omega^\infty agree. This comparison is then used to show that two
different constructions of the spectrum of units gl_1 R of a commutative ring
spectrum R agree.Comment: 62 pages. The definition of the functor \mathbb{Q} is changed.
Sections 8, 9, 17 and 18 contain revisions and/or new materia
Automatic Repair of Infinite Loops
Research on automatic software repair is concerned with the development of
systems that automatically detect and repair bugs. One well-known class of bugs
is the infinite loop. Every computer programmer or user has, at least once,
experienced this type of bug. We state the problem of repairing infinite loops
in the context of test-suite based software repair: given a test suite with at
least one failing test, generate a patch that makes all test cases pass.
Consequently, repairing infinites loop means having at least one test case that
hangs by triggering the infinite loop. Our system to automatically repair
infinite loops is called . We develop a technique to manipulate
loops so that one can dynamically analyze the number of iterations of loops;
decide to interrupt the loop execution; and dynamically examine the state of
the loop on a per-iteration basis. Then, in order to synthesize a new loop
condition, we encode this set of program states as a code synthesis problem
using a technique based on Satisfiability Modulo Theory (SMT). We evaluate our
technique on seven seeded-bugs and on seven real-bugs. is able to
repair all of them, within seconds up to one hour on a standard laptop
configuration
Semi-infinite cohomology and superconformal algebras
We describe representations of certain superconformal algebras in the
semi-infinite Weil complex related to the loop algebra of a complex
finite-dimensional Lie algebra and in the semi-infinite cohomology. We show
that in the case where the Lie algebra is endowed with a non-degenerate
invariant symmetric bilinear form, the relative semi-infinite cohomology of the
loop algebra has a structure, which is analogous to the classical structure of
the de Rham cohomology in K\"ahler geometry.Comment: 23 pages, TeX. To be published in Annales de l'Institut Fourie
The Picard group of the loop space of the Riemann sphere
The loop space of the Riemann sphere consisting of all C^k or Sobolev W^{k,p}
maps from the circle S^1 to the sphere is an infinite dimensional complex
manifold. We compute the Picard group of holomorphic line bundles on this loop
space as an infinite dimensional complex Lie group with Lie algebra the first
Dolbeault group. The group of Mobius transformations G and its loop group LG
act on this loop space. We prove that an element of the Picard group is
LG-fixed if it is G-fixed; thus completely answer the question by Millson and
Zombro about G-equivariant projective embedding of the loop space of the
Riemann sphere.Comment: International Journal of Mathematic
Infinite loop spaces and nilpotent K-theory
Using a construction derived from the descending central series of the free
groups, we produce filtrations by infinite loop spaces of the classical
infinite loop spaces , , , , , and
. We show that these infinite loop spaces are the zero
spaces of non-unital -ring spectra. We introduce the notion of
-nilpotent K-theory of a CW-complex for any , which extends the
notion of commutative K-theory defined by Adem-G\'omez, and show that it is
represented by , were is the -th term of
the aforementioned filtration of .
For the proof we introduce an alternative way of associating an infinite loop
space to a commutative -monoid and give criteria when it can be
identified with the plus construction on the associated limit space.
Furthermore, we introduce the notion of a commutative -rig and show
that they give rise to non-unital -ring spectra.Comment: To appear in Algebraic and geometric topolog
- …