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Journal ArticleDOI

M-Brane Models and Loop Spaces

TL;DR: In this article, an extension of the ADHMN construction of monopoles to M-brane models is presented, which gives a map from solutions to the Basu-Harvey equation to solutions to self-dual string equation transgressed to loop space.
Abstract: I review an extension of the ADHMN construction of monopoles to M-brane models. This extended construction gives a map from solutions to the Basu-Harvey equation to solutions to the self-dual string equation transgressed to loop space. Loop spaces appear in fact quite naturally in M-brane models. This is demonstrated by translating a recently proposed M5-brane model to loop space. Finally, I comment on some recent developments related to the loop space approach to M-brane models.

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Citations
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Journal ArticleDOI
TL;DR: The duality-symmetric actions for a large class of six-dimensional models describing hierarchies of non-Abelian scalar, vector and tensor fields related to one another by first-order (self-)duality equations that follow from these actions were constructed in this article.
Abstract: We construct the duality-symmetric actions for a large class of six-dimensional models describing hierarchies of non-Abelian scalar, vector and tensor fields related to one another by first-order (self-)duality equations that follow from these actions. In particular, this construction provides a Lorentz invariant action for non-Abelian self-dual tensor fields. The class of models includes the bosonic sectors of the $6d$ (1,0) superconformal models of interacting non-Abelian self-dual tensor, vector, and hypermultiplets.

42 citations

Journal ArticleDOI
TL;DR: In this article, an alternative form of the M5-brane action in which the sixdimensional world volume is subject to a covariant split into 3+3 directions by a triplet of auxiliary fields is presented.
Abstract: We construct an alternative form of the M5-brane action in which the sixdimensional worldvolume is subject to a covariant split into 3+3 directions by a triplet of auxiliary fields. We consider the relation of this action to the original form of the M5-brane action and to a Nambu-Poisson 5-brane action based on the Bagger-Lambert-Gustavsson model with the gauge symmetry of volume preserving diffeomorphisms.

40 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the non-abelian self-dual string problem for an arbitrary number of M 2-M 5 branes and constructed a solution with an arbitrary N petertodd 2 unit of selfdual charges.
Abstract: We consider the non-abelian theory [1] for an arbitrary number N 5 of five-branes and construct self-dual string solution with an arbitrary N 2 unit of self-dual charges. This generalizes the previous solution of non-abelian self-dual string [2] of N 5 = 2, N 2 = 1. The radius-transverse distance relation describing the M2-branes spike, particularly its dependence on N 2 and N 5, is obtained and is found to agree precisely with the supergravity description of an intersecting M2-M5 branes system.

27 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider the non-abelian self-dual two-form theory arXiv:1203.4224 and find new exact solutions for the MW/M5 system with instantons in 4-dimensions and describe wave moving in null directions.
Abstract: We consider the non-abelian self-dual two-form theory arXiv:1203.4224 and find new exact solutions. Our solutions are supported by Yang-Mills (anti)instantons in 4-dimensions and describe wave moving in null directions. We argue and provide evidence that these instanton string solutions correspond to M-wave (MW) on the worldvolume of multiple M5-branes. When dimensionally reduced on a circle, the MW/M5 system is reduced to the D0/D4 system with the D0-branes represented by the Yang-Mills instanton of the D4-branes Yang-Mills gauge theory. We show that this picture is precisely reproduced by the dimensional reduction of our instanton string solutions.

14 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the non-abelian self-dual string problem for an arbitrary number of five-branes and constructed a solution with an arbitrary $N_2$ unit of selfdual charges.
Abstract: We consider the non-abelian theory (http://arxiv.org/abs/arXiv:1203.4224) for an arbitrary number $N_5$ of five-branes and construct self-dual string solution with an arbitrary $N_2$ unit of self-dual charges. This generalizes the previous solution of non-abelian self-dual string (http://arxiv.org/abs/arXiv:1207.1095) of $N_5=2, N_2=1$. The radius-transverse distance relation describing the M2-branes spike, particularly its dependence on $N_2$ and $N_5$, is obtained and is found to agree precisely with the supergravity description of an intersecting M2-M5 branes system.

4 citations

References
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Posted Content
TL;DR: In this article, the authors give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six dimensions.
Abstract: The goal of these notes is to give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six dimensions.

40 citations

Journal ArticleDOI
TL;DR: In this article, an ADHMN-like construction was proposed to generate self-dual string solutions to the effective M5-brane world volume theory from solutions to Basu-Harvey equation.
Abstract: We present an ADHMN-like construction which generates self-dual string solutions to the effective M5-brane worldvolume theory from solutions to the Basu-Harvey equation. Our construction finds a natural interpretation in terms of gerbes, which we develop in some detail. We also comment on a possible extension to stacks of multiple M5-branes.

36 citations

Journal ArticleDOI
TL;DR: In this paper, an ADHMN-like construction was proposed to generate self-dual string solutions to the effective M5-brane world volume theory from solutions to Basu-Harvey equation.
Abstract: We present an ADHMN-like construction which generates self-dual string solutions to the effective M5-brane worldvolume theory from solutions to the Basu-Harvey equation. Our construction finds a natural interpretation in terms of gerbes, which we develop in some detail. We also comment on a possible extension to stacks of multiple M5-branes.

35 citations

Journal Article
TL;DR: In this article, the authors introduce and study categorified global holonomy in the form of 2-bundles with 2-holonomy, and show how these relate to nonabelian gerbes.
Abstract: Lifting supersymmetric quantum mechanics to loop space yields the superstring. A particle charged under a fiber bundle thereby turns into a string charged under a 2-bundle, or gerbe. This stringification is nothing but categorification. We look at supersymmetric quantum mechanics on loop space and demonstrate how deformations here give rise to superstring background fields and boundary states, and, when generalized, to local nonabelian connections on loop space. In order to get a global description of these connections we introduce and study categorified global holonomy in the form of 2-bundles with 2-holonomy. We show how these relate to nonabelian gerbes and go beyond by obtaining global nonabelian surface holonomy, thus providing a class of action functionals for nonabelian strings. The examination of the differential formulation, which is adapted to the study of nonabelian p-form gauge theories, gives rise to generalized nonabelian Deligne hypercohomology. The (possible) relation of this to strings in Kalb-Ramond backgrounds, to M2/M5-brane systems, to spinning strings and to the derived category description of D-branes is discussed. In particular, there is a 2-group related to the String-group which should be the right structure 2-group for the global description of spinning strings.

27 citations

Posted Content
TL;DR: In this paper, a 2-plectic manifold can be reduced to ordinary quantization of its loop space, which is a symplectic manifold, and the latter can be quantized using groupoids.
Abstract: We review the various contexts in which quantized 2-plectic manifolds are expected to appear within closed string theory and M-theory. We then discuss how the quantization of a 2-plectic manifold can be reduced to ordinary quantization of its loop space, which is a symplectic manifold. We demonstrate how the latter can be quantized using groupoids. After reviewing the necessary background, we present the groupoid quantization of the loop space of R^3 in some detail.

24 citations