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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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
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
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
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
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
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TL;DR: In this paper, the authors studied the correspondence between IIb solitonic 1-branes and monopoles in the context of the 3-brane realization of the super Yang-Mills theory.
Abstract: We study the correspondence between IIb solitonic 1-branes and monopoles in the context of the 3-brane realization of $D=4$ $N=4$ super Yang-Mills theory. We show that a bound state of 1-branes stretching between two separated 3-branes exhibits a family of super-symmetric ground states that can be identified with the ADHMN construction of the moduli space of $SU(2)$ monopoles.. This identification is supported by the construction of the monopole gauge field as a space-time coupling in the quantum mechanical effective action of a 1-brane used as a probe. The analysis also reveals an intriguing aspect of the 1-brane theory:the transverse oscillations of the 1-branes in the ground states are described by non-commuting matrix valued fields which develop poles at the boundary. Finally, the construction is generalized to $SU(n)$ monopoles with arbitrary $n>2$.
235 citations
TL;DR: In this article, a BPS soliton of the M theory fivebrane's equations of motion representing a supersymmetric self-dual string was obtained and the resulting solution was then dimensionally reduced and used to obtain 0-brane and (p-2)-brane solitons on D-p-branes.
Abstract: We obtain a BPS soliton of the M theory fivebrane's equations of motion representing a supersymmetric self-dual string. The resulting solution is then dimensionally reduced and used to obtain 0-brane and (p-2)-brane solitons on D-p-branes.
214 citations
TL;DR: In this paper, the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way are discussed. But the main focus is on the 3-Lie algebra structure.
Abstract: This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two entries Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. Three-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert- Gustavsson model. Because of this, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations (it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A4 model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization.
212 citations
TL;DR: In this article, a generalization of the Bagger-Lambert-Gustavsson action is proposed for the description of an arbitrary number of M2-branes.
Abstract: We propose a generalization of the Bagger-Lambert-Gustavsson action as a candidate for the description of an arbitrary number of M2-branes. The action is formulated in terms of N=2 superfields in three dimensions and corresponds to an extension of the usual superfield formulation of Chern-Simons matter theories. Demanding gauge invariance of the resulting theory does not imply the total antisymmetry of the underlying 3-Lie algebra structure constants. We relax this condition and propose a class of examples for these generalized 3-Lie algebras. We also discuss various associated ordinary Lie algebras.
137 citations
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TL;DR: In this paper, lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles are presented, based on lectures given in March 2010 at the Chinese University of Hong Kong.
Abstract: These are lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles. They are based on lectures given in March 2010 at the Chinese University of Hong Kong.
133 citations