Related papers: Octonions, G_2 and generalized Lie 3-algebras

The purpose of this study is to extend the concept of a generalized Lie $3-$ algebra, known to the divisional algebra of the octonions $\mathbb{O}$, to split-octonions $\mathbb{SO}$, which is non-divisional. This is achieved through the…

A magnetic quiver framework is proposed for studying maximal branches of 3d orthosymplectic Chern--Simons matter theories with $\mathcal{N} \geq 3$ supersymmetry, arising from Type IIB brane setups with O3 planes. These branches are…

A new structure, based on joining copies of a group by means of a \emph{twist}, has recently been considered to describe the brackets of the two exceptional real Lie algebras of type $G_2$ in a highly symmetric way. In this work we show…

We compute the form of the Lagrangian of N=1 supersymmetric theories with gauged axion symmetries. It turns out that there appear generalized Chern-Simons terms that were not considered in previous superspace formulations of general N=1…

Since the pioneering work of Bagger-Lambert and Gustavsson, there has been a proliferation of three-dimensional superconformal Chern-Simons theories whose main ingredient is a metric 3-algebra. On the other hand, many of these theories have…

We consider D=3 supersymmetric Chern-Simons gauge theories both from the point of view of their formal structure and of their applications to the $\mathrm{AdS_4/CFT_3}$ correspondence. From the structural view-point, we use the new…

We construct several examples of (2+1) dimensional N=2 supersymmetric Chern-Simons theories, whose moduli space is given by non-compact toric Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT. One such example is…

Motivated by the recent proposal of an N=8 supersymmetric action for multiple M2-branes, we study the Lie 3-algebra in detail. In particular, we focus on the fundamental identity and the relation with Nambu-Poisson bracket. Some new…

We study observables and deformations of generalized Chern-Simons action and show how to apply these results to maximally supersymmetric gauge theories. We describe a construction of large class of deformations based on some results on the…

We study three-dimensional gauge theories based on orthogonal groups. Depending on the global form of the group these theories admit discrete $\theta$-parameters, which control the weights in the sum over topologically distinct gauge…

We discuss a generalization of Chern-Simons theory in three dimensions based on Leibniz (or Loday) algebras, which are generalizations of Lie algebras. Special cases of such theories appear in gauged supergravity, where the Leibniz algebra…

We study a system of N D2-branes probing a generic Calabi-Yau three-fold singularity in the presence of a non-zero quantized Romans mass n. We argue that the low-energy effective N = 2 Chern-Simons quiver gauge theory flows to a…

We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on…

We propose a duality for N=2 d=3 Chern-Simons gauge theories with orthogonal gauge groups and matter in the vector representation. This duality generalizes level-rank duality for pure Chern-Simons gauge theories with orthogonal gauge groups…

We systematically study 3d $\mathcal{N}=2$ dualities for $U(N_c)$ gauge theories with different CS levels for the abelian and the non-abelian factors. We derive such dualities by a gauging/ungauging procedure on other known dualities and by…

A generalization of Chern-Simons gauge theory is formulated in any dimension and arbitrary gauge group where gauge fields and gauge parameters are differential forms of any degree. The quaternion algebra structure of this formulation is…

We use superalgebras to realize the 3-algebras used to construct N=6, 8 Chern-Simons-matter (CSM) theories. We demonstrate that the superalgebra realization of the 3-algebras provides a unified framework for classifying the gauge groups of…

We generalize the Giveon-Kutasov duality by adding possible Chern-Simons interactions for the $U(N)$ gauge group. Some of the generalized dualities are known in the literature and many others are new to the best of our knowledge. The…

We study a three-dimensional N=3 U(N)_k x U(N)_{-k} Chern-Simons matter theory with flavour, corresponding to the N=6 Aharony-Bergman-Jafferis-Maldacena CSM theory coupled to 2N_f fundamental fields. The dual holographic description is…

Compactification of M- / string theory on manifolds with $G_2$ structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a…