Related papers: Algebraic vs physical N=6 3-algebras
We propose a graphic method to derive the classical algebra (Dirac brackets) of non-local conserved charges in the two dimensional supersymmetric non-linear $O(N)$ sigma model. As in the purely bosonic theory we find a cubic Yangian…
We generalize the free Fermi-gas formulation of certain 3d ${\cal N}=3$ supersymmetric Chern-Simons-matter theories by allowing Fayet-Iliopoulos couplings as well as mass terms for bifundamental matter fields. The resulting partition…
We propose a generalization of non-commutative geometry and gauge theories based on ternary Z_3-graded structures. In the new algebraic structures we define, we leave all products of two entities free, imposing relations on ternary products…
Aharony, Bergman, Jafferis and Maldacena have recently proposed a dual gravitational description for a family of superconformal Chern Simons theories in three spacetime dimensions. In this note we perform the one loop computation that…
We introduce a class of 3d theories consisting of strongly-coupled ${\mathcal N}=4$ systems coupled to ${\mathcal N}=3$ Chern-Simons gauge multiplets, which exhibit ${\mathcal N}=4$ enhancements when a peculiar condition on the Chern-Simons…
3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. The paper concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such…
Revisiting the results by Winternitz [Symmetry in physics, CRM Proc. Lecture Notes 34, American Mathematical Society, Providence, RI, 2004, pp. 215-227], we thoroughly refine his classification of Lie subalgebras of the real order-three…
A classification of the semisimple subalgebras of the Lie algebra of traceless $3\times 3$ matrices with complex entries, denoted $A_2$, is well-known. We classify its nonsemisimple subalgebras, thus completing the classification of the…
We classify simple linearly compact n-Lie superalgebras with n>2 over a field F of characteristic 0. The classification is based on a bijective correspondence between non-abelian n-Lie superalgebras and transitive Z-graded Lie superalgebras…
Extending previous work that involved D3-branes ending on a fivebrane with $\theta_{\mathrm{YM}}\not=0$, we consider a similar two-sided problem. This construction, in case the fivebrane is of NS type, is associated to the three-dimensional…
An algebraic classification of complex $5$-dimensional nilpotent commutative $\mathfrak{CD}$-algebras is given. This classification is based on an algebraic classification of complex $5$-dimensional nilpotent Jordan algebras.
We study the algebra of BPS Wilson loops in 3d gauge theories with N=2 supersymmetry and Chern-Simons terms. We argue that new relations appear on the quantum level, and that in many cases this makes the algebra finite-dimensional. We use…
We study a series of real nonassociative algebras $\mathbb{O}_{p,q}$ introduced in $[5]$. These algebras have a natural $\mathbb{Z}_2^n$-grading, where $n=p+q$, and they are characterized by a cubic form over the field $\mathbb{Z}_2$. We…
We consider the 4-dimensional $\mathcal{N}=1$ Lie superconformal algebra and search for completely "symmetric" (in the graded sense) 3-index invariant tensors. The solution we find is unique and we show that the corresponding invariant…
We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N=4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N=4,…
This paper is devoted to the complete algebraic and geometric classification of complex $4$-dimensional nilpotent left-symmetric algebras. The corresponding geometric variety has dimension $15$ and decomposes into $3$ irreducible components…
Three-dimensional conformal theories with six supersymmetries and SU(4) R-symmetry describing stacks of M2-branes are here proposed to be related to generalized Jordan triple systems. Writing the four-index structure constants in an…
The topological supersymmetry of the pure Chern-Simons model in three dimensions is established in the case where the theory is defined in the axial gauge.
We explore $\mathcal{N}=1$ supersymmetric extensions of algebras going beyond the Poincar\'e and AdS ones in three spacetime dimensions. Besides reproducing two known examples, we present new superalgebras, which all correspond to…
A class of associative (super) algebras is presented, which naturally generalize both the symmetric algebra $Sym(V)$ and the wedge algebra $\wedge (V)$, where $V$ is a vector-space. These algebras are in a bijection with those subsets of…