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.
Citations
More filters
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
More filters
TL;DR: An introduction to the theory of bundle gerbes and their relationship to Hitchin-Chatterjee gerbes is presented in this paper, where connective structures, triviality and stable isomorphism as well as examples and applications are discussed.
Abstract: An introduction to the theory of bundle gerbes and their relationship to Hitchin-Chatterjee gerbes is presented. Topics covered are connective structures, triviality and stable isomorphism as well as examples and applications.
79 citations
TL;DR: In this paper, 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.
72 citations
Posted Content•
TL;DR: In this paper, it was shown that the Kac-moody symmetry induces a U(N)x U(n) gauge symmetry in the theory of N coincident M5-branes.
Abstract: The Chern-Simon action of the ABJM theory is not gauge invariant in the presence of a boundary. In the paper arXiv:0909.2333, this was shown to imply the existence of a Kac-Moody symmetry on the theory of multiple self-dual strings. In this paper we conjecture that the Kac-Moody symmetry induces a U(N)x U(N) gauge symmetry in the theory of N coincident M5-branes. As a start, we construct this G x G gauge symmetry algebra structure which naturally includes the tensor gauge transformation for a non-abelian 2-form tensor gauge field. This new G x G gauge structure allows us to write down a theory of a non-abelian tensor gauge field readily. For application to multiple M5-branes, we note that the field content of the G x G non-abelian tensor gauge theory can be fitted nicely as (1,0) supermultiplets; and we suggest a construction of the theory of multiple M5-branes with manifest (1,0) supersymmetry.
71 citations
TL;DR: In this article, the authors discuss chiral zero-rest-mass field equations on six-dimensional space-time from a twistorial point of view, and present a detailed cohomological analysis, develop both Penrose and Penrose-Ward transforms, and analyse the corresponding contour integral formulae.
Abstract: We discuss chiral zero-rest-mass field equations on six-dimensional space-time from a twistorial point of view. Specifically, we present a detailed cohomological analysis, develop both Penrose and Penrose-Ward transforms, and analyse the corresponding contour integral formulae. We also give twistor space action principles. We then dimensionally reduce the twistor space of six-dimensional space-time to obtain twistor formulations of various theories in lower dimensions. Besides well-known twistor spaces, we also find a novel twistor space amongst these reductions, which turns out to be suitable for a twistorial description of self-dual strings. For these reduced twistor spaces, we explain the Penrose and Penrose-Ward transforms as well as contour integral formulae.
65 citations
TL;DR: In this article, the boundary conditions in Nahm's equations were derived by considering a system of N parallel D1-branes perpendicular to a D3-brane in type IIB string theory.
Abstract: We derive certain boundary conditions in Nahm's equations by considering a system of N parallel D1-branes perpendicular to a D3-brane in type IIB string theory.
63 citations