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Loop space
About: Loop space is a research topic. Over the lifetime, 1091 publications have been published within this topic receiving 20868 citations.
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TL;DR: In this paper, a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n, and they are interpreted using string theory and presented some partial proofs of this conjecture.
Abstract: Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n We interpret these ideas using string theory and present some partial proofs of this conjecture We then extend the notion of bags and their Nahm transform to higher gauge theories and arbitrary domains Bags in four dimensions conjecturally describe the large n limit of n self-dual strings We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space We also formulate our Nahm equations using strong homotopy Lie algebras
567 citations
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TL;DR: In this paper, the authors provide some background to the theory of operads, used in the first author's papers on 2D topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th /9305013).
Abstract: This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended for specialists.
526 citations
TL;DR: In this paper, the classical membrane fields should be taken values in a loop algebra, such as a loop space version of the Nahm equations, and the authors showed that there appears to be no infinite set of finite-dimensional Lie algebras (such as su(N) for any N) that satisfy the algebraic structure of the membrane theory.
Abstract: We give two independent arguments why the classical membrane fields should be take values in a loop algebra The first argument comes from how we may construct selfdual strings in the M5 brane from a loop space version of the Nahm equations The second argument is that there appears to be no infinite set of finite-dimensional Lie algebras (such as su(N) for any N) that satisfies the algebraic structure of the membrane theory
334 citations
TL;DR: In this article, the projective limit of a projective family of compact Hausdorff manifolds, labelled by graphs, is considered, and the notion of differential geometry is introduced.
331 citations
TL;DR: In this paper, the authors define iterated integrals 5w... w, where wl, *., w, are 1-forms and wl is a form of degree Pi + * -1+ Prr on a differentiable manifold.
Abstract: We continue to define iterated integrals 5w ... w, where wl, *., w, are 1forms. Such iterated integrals will be defined for forms wi, *-*, w, of arbitrary degrees on a differentiable manifold or, more generally, a suitably defined "differentiable space". The space P(X) of piecewise smooth paths on a differentiable manifold X turns out to be a differentiable space. If wi, *.., w, are forms of respective degrees P1, ..., Pr on X, then the iterated integral Wi .. Wr is a form of degree Pi + * -1+ Prr on P(X). Let P(X; x0, xl) denote the subspace of P(X) consisting of paths from a given point x0 to another given point xl. We are interested in those iterated integrals or linear combinations of iterated integrals, which give rise to de Rham cohomology classes of QSX = P(X; x0, x0) and shall prove an iterated integral version of a loop space de Rham theorem, which includes the following
285 citations