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
References
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TL;DR: In this paper, the authors studied the higher-dimensional Penrose transform between conformally invariant massless fields on space-time and cohomology classes on twistor space, defined to be the space of projective pure spinors of the conformal group.
61 citations
TL;DR: In this paper, a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time was established.
Abstract: We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0) supersymmetric non-Abelian constraint equations containing the tensor multiplet. We also demonstrate how this construction leads to constraint equations for non-Abelian supersymmetric self-dual strings.
61 citations
TL;DR: In this article, it was shown that the Nahm transform over flat tori is a duality transform, and that it can not be used to construct instantons over the first Brillouin zone.
Abstract: Recently P. Braam pointed out that Nahm's adaption of the ADHM procedure to the case of monopoles equally well applies to instantons over flat tori, relating them to instantons over the first Brillouin zone. We show that this construction has an inverse. Hence the Nahm transform actually is a duality transform.
54 citations
TL;DR: In this article, the authors make the observation that M-brane models defined in terms of 3-algebras can be interpreted as higher gauge theories involving Lie 2-groups.
Abstract: We make the observation that M-brane models defined in terms of 3-algebras can be interpreted as higher gauge theories involving Lie 2-groups. Such gauge theories arise in particular in the description of non-abelian gerbes. This observation allows us to put M2- and M5-brane models on equal footing, at least as far as the gauge structure is concerned. Furthermore, it provides a useful framework for various generalizations; in particular, it leads to a fully supersymmetric generalization of a previously proposed set of tensor multiplet equations.
51 citations
TL;DR: In this article, the authors discuss the inherent difficulties pertaining to a maximally supersymmetric lagrangian formulation with the appropriate field content and symmetries, and discuss how introducing the concept of 3-algebras allows for such a description.
Abstract: We review developments in the theory of multiple, parallel membranes in M-theory. After discussing the inherent difficulties pertaining to a maximally supersymmetric lagrangian formulation with the appropriate field content and symmetries, we discuss how introducing the concept of 3-algebras allows for such a description. Different choices of 3-algebras lead to distinct classes of 2+1 dimensional theories with varying degrees of supersymmetry. We then describe how these are equivalent to a type of conventional superconformal Chern-Simons gauge theories at level k, coupled to bifundamental matter. Analysing the physical properties of these theories leads to the identification of a certain subclass of models with configurations of M2-branes in Z_k orbifolds of M-theory. In addition these models give rise to a whole new sector of the gauge/gravity duality in the form of an AdS_4/CFT_3 correspondence. We also discuss mass deformations, higher derivative corrections as well as the possibility of extracting information about M5-brane physics.
42 citations