Related papers: Little Groups and Statistics of Branes
We present here the AdS generalization of BPS preons, which were introduced as the hypothetical constituents of M-theory preserving all but one supersymmetries. Our construction, suggested by the relation of `lower dimensional preons' with…
A static minimal energy configuration of a super p-brane in a supersymmetric (n+1)-dimensional spacetime is shown to be a `generalized calibrated' submanifold. Calibrations in $\bE^{(1,n)}$ and $AdS_{n+1}$ are special cases. We present…
In the Born-Infeld 'harmonic gauge' description of M-branes moving in R^{M+1} the underlying M+2 dimensional Poincare - invariance gives rise to an interesting system of conservation laws showing signs of integrability.
We derive the spacetime superalgebras explicitly from ``test'' M-brane actions in M-brane backgrounds to the lowest order in $\theta$ via canonical formalism, and discuss various BPS saturated configurations on the basis of their central…
The representation theory of left regular band semigroup algebras is well-studied and known to have close connections with combinatorial topology, as established in the work of Margolis--Saliola--Steinberg ('15, '21). In this paper, we…
Configurations of two or more branes wrapping different homology cycles of space-time are considered and the amount of supersymmetry preserved is analysed, generalising the analysis of multiple branes in flat space. For K3…
We describe how one may use either the superPoincar\'e algebra or the exceptional algebra to construct maximal supergravity theories in the light-cone formalism. The d=4 construction shows both symmetries albeit in a non-linearly realized…
We construct the covariant, spinor sets of relativistic wave equations for a massless field on the basis of the two copies of the R-deformed Heisenberg algebra. For the finite-dimensional representations of the algebra they give a universal…
We show that all spin groups of non-definite, quinary quadratic forms over a field with characteristic 0 can be represented as 2 by 2 matrices with entries in an associated quaternion algebra. Over local and global fields, we further study…
In order to avoid the difficulties encountered by relativistic quantum theory of single particles, we pursue a deductive development of the theory from physical principles, without canonical quantization, by making use of group-theoretical…
Massive arbitrary spin supermultiplets and massless (scalar and spin one-half) supermultiplets of the N=2 Poincare superalgebra in three-dimensional flat space are considered. Both the integer spin and half-integer spin supermultiplets are…
We study invariant theory of the general linear supergroup in positive characteristic. In particular, we determine when the symmetric group algebra acts faithfully on tensor superspace and demonstrate that the symmetric group does not…
Using the theory of fibre bundles, we provide several equivalent intrinsic descriptions for the Hilbert spaces of $n$ ``free'' nonrelativistic and relativistic plektons in two space dimensions. These spaces carry a ray representation of the…
We present two classes of regular supergravity backgrounds dual to supersymmetric and non-supersymmetric gauge theories living on the world-volume of wrapped branes. In particular we consider the Maldacena Nunez and the Klebanov Strassler…
We pursue an analogy of the Schur-Weyl reciprocity for the spinor groups and pick up the irreducible spin representations in the tensor space $\Delta \textstyle{\bigotimes \bigotimes^k V}$. Here $\Delta$ is the fundamental representation of…
We consider a construction of the fundamental spin representations of the simple Lie algebras $\mathfrak{so}(n)$ in terms of binary arithmetic of fixed width integers. This gives the spin matrices as a Lie subalgebra of a…
We start with the Lorentz algebra $ L=o_{R}(1,3)$ over the reals and find a suitable basis $B$ relative to which the structure constants are integers. Thus we consider the $Z$-algebra $L_{Z}$ which is free as a $Z$-module and its $Z$-basis…
We construct a novel higher-spin theory of gravity in 2+1 spacetime dimensions. The construction is based on a higher-spin super-algebra extending the Poincare group. Our algebra accommodates all integer and half-integer spins from 1 to…
The notion of Wigner particles is attached to irreducible unitary representations of the Poincare group, characterized by parameters m and s of mass and spin, respectively. However, the Lorentz symmetry is broken in theories with long-range…
We generalise the definition of a group algebra so that it makes sense for non-locally compact topological groups, in particular, we require that the representation theory of the group algebra is isomorphic (in the sense of Gelfand-Raikov)…