Related papers: M2 to D2 and vice versa by 3-Lie and Lie bialgebra
We study Lie bialgebra structures on \emph{flat metric Lie algebras}, that is, Lie algebras $(\mathfrak{g},\langle\cdot,\cdot\rangle)$ whose associated left-invariant Riemannian metric on the simply connected Lie group $G$ has zero…
We continue our study of BPS equations and supersymmetric configurations in the Bagger-Lambert theory. The superalgebra allows three different types of central extensions which correspond to compounds of various M-theory objects: M2-branes,…
Gauging the M-2-brane effective action with respect to an Abelian isometry in such a way that the invariance under gauge transformations of the 3-form potential is maintained (slightly modified) we obtain a fully covariant action with…
In this short communication we show how the Lie algebra $\mathfrak{g}_2$ can easily be described as a free Lie algebra on 3 generators, subject to some simple quadruple relations for these generators.
In this paper the usual $Z_2$ graded Lie algebra is generalized to a new form, which may be called $Z_{2,2}$ graded Lie algebra. It is shown that there exists close connections between the $Z_{2,2}$ graded Lie algebra and parastatistics, so…
We construct the interaction terms between the world-volume fields of multiple M2-branes and the 3- and 6-form fields in the context of ABJM theory with U($N$)$\times$U($N$) gauge symmetry. A consistency check is made in the simplest case…
Four- and six-dimensional Drinfeld doubles were classified in the past in terms of Manin triples. We provide an important step towards the classification of eight-dimensional Drinfeld doubles by presenting an extensive list of Manin triples…
Classical r-matrices of the three-dimensional real Lie bialgebras are obtained. In this way all three-dimensional real coboundary Lie bialgebras and their types (triangular, quasitriangular or factorizable) are classified. Then, by using…
Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a…
As Lie algebras of compact connected Lie groups, semisimple Lie algebras have wide applications in the description of continuous symmetries of physical systems. Mathematically, semisimple Lie algebra admits a Cartan-Weyl basis of generators…
This paper investigates M-brane quantum geometry (and its representation by equations involving the 3-bracket) by looking at the compactification of an M-brane system to a D-brane system. Particularly of interest is the system where…
T-branes are exotic bound states of D-branes, characterized by mutually non-commuting vacuum expectation values for the worldvolume scalars. The M/F-theory geometry lifting D6/D7-brane configurations is blind to the T-brane data. In this…
Two types of higher order Lie $\ell$-ple systems are introduced in this paper. They are defined by brackets with $\ell > 3$ arguments satisfying certain conditions, and generalize the well known Lie triple systems. One of the…
In the last few years, brane tilings have proven to be an efficient and convenient way of studying supersymmetric gauge theories living on D3-branes or M2-branes. In these pages we present a quick and simple introduction to the subject,…
We show that M-theory on spaces with irreducible holonomy represent Type IIA backgrounds in which a collection of D6-branes wrap a supersymmetric cycle in a manifold with a holonomy group different from the one appearing in the M-theory…
The construction of Lie bialgebra from double Lie algebra is presented. It is used to relate some types of cobracket on inhomogenous so(p,q) algebras with double Lie algebra structures on so(p+1,q) or so(p,q+1). Also it is shown that the…
We classify canonical metric 3-algebra structures on matrix algebras and find novel three-dimensional conformally invariant actions in N=4 projective superspace based on them. These can be viewed as Chern-Simons theories with special matter…
We analyze the coulomb branch of the non-unitary Lorentzian three algebra theory that has been proposed as a possible candidate for describing the world volume theory of multiple M2-branes. In order that it describes the theory of multiple…
In this talk we will review the construction of M2-brane SCFT's highlighting some novelties and the role of 3-algebras. Parts of our discussion will closely follow parts of arXiv:1203.3546. Next we will discuss M5-branes: the basics, the…
We show how to cast an interacting system of M--branes into manifestly gauge-invariant form using an arrangement of higher-dimensional Dirac surfaces. Classical M--theory has a cohomologically nontrivial and noncommutative set of gauge…