Related papers: Triality of Majorana-Weyl Spacetimes with Differen…
Majorana-Weyl spacetimes offer a rich algebraic setup and new types of space-time dualities besides those discussed by Hull. The triality automorphisms of Spin(8) act non-trivially on Majorana-Weyl representations and Majorana-Weyl…
Higher dimensional Majorana-Weyl spacetimes present space-time dualities which are induced by the Spin(8) triality automorphisms. Different signature versions of theories such as 10-dimensional SYM's, superstrings, five-branes, F-theory,…
The properties of Dirac gamma matrices in a four-dimensional space-time with the $(2,2)$ signature are studied. The basic spinors are classified, and the existence of Majorana-Weyl spinors is noted. Supersymmetry in $2 + 2$ dimensions is…
We study supersymmetry and self-duality in a four-dimensional space-time with the signature (2,2), that we call the Atiyah-Ward space-time. Dirac matrices and spinors, in particular Majorana-Weyl spinors, are investigated in detail. We…
Versions of M-theory are found in spacetime signatures (9,2) and (6,5), in addition to the usual M-theory in 10+1 dimensions, and these give rise to type IIA string theories in 10-dimensional spacetime signatures (10,0),(9,1),(8,2),(6,4)…
Duality symmetries in M--theory and string theory are reviewed, with particular emphasis on the way in which string winding modes and brane wrapping modes can lead to new spatial dimensions. Brane world-volumes wrapping around Lorentzian…
Eight Majorana fermions in $d=1+1$ dimensions enjoy a triality that permutes the representation of the $SO(8)$ global symmetry in which the fermions transform. This triality plays an important role in the quantization of the superstring,…
Duality groups of Abelian gauge theories on four manifolds and their reduction to two dimensions are considered. The duality groups include elements that relate different space-times in addition to relating different gauge-coupling…
A pseudoclassical theories of Majorana, Weyl and Majorana--Weyl particles in the space--time dimensions $D=2n$ are constructed. The canonical quantization of these theories is carried out and as a result we obtain the quantum mechanical…
Superconformal algebras embedding space-time in any dimension and signature are considered. Different real forms of the $R$-symmetries arise both for usual space-time signature (one time) and for Euclidean or exotic signatures (more than…
String theory, specifically type-II superstring theory, can be formulated in any ten-dimensional signature. To facilitate the study of supergravity and superstring theories in this setting, we present a uniform construction of supersymmetry…
By analyzing super-torsion and brane super-cocycles, we derive a new duality in M-theory, which takes the form of a higher version of T-duality in string theory. This involves a new topology change mechanism abelianizing the 3-sphere…
We discuss the signature of space-time in the context of the E_11 -conjecture. In this setting, the space-time signature depends on the choice of basis for the ``gravitational sub-algebra'' A_10, and Weyl transformations connect…
Weyl superconductors feature Weyl points at zero energy in the three-dimensional (3D) Brillouin zone and arc states that connect the projections of these Weyl points on the surface. We report that higher-order Weyl superconductors can be…
General considerations on the unification of A-type and B-type supersymmetries in the context of interacting p-branes strongly suggest that the signature of spacetime includes two timelike dimensions. This leads to the puzzle of how…
The hypothesis that the causal properties of space-time, as well as other properties of physical systems like unitarity, charge conservation, etc., might be decided by the higher dimensional structure (in particular, higher-dimensional…
A global superalgebra with 32 supercharges and all possible central extensions is studied in order to extract some general properties of duality and hidden dimensions in a theory that treats $p$-branes democratically. The maximal number of…
The $N=2$ supersymmetric {\it self-dual} Yang-Mills theory and the $N=4$ and $N=2$ {\it self-dual} supergravities in $2+2$ space-time dimensions are formulated for the first time. These formulations utilize solutions of the Bianchi…
It is shown that causal automorphisms on two-dimensional Minkowski spacetime can be characterized by the invariance of the wave equations.
Through timelike dualities, one can generate exotic versions of $M$-theory with different spacetime signatures. These are the $M^*$-theory with signature $(9,2,-)$, the $M'$-theory, with signature $(6,5,+)$ and the theories with reversed…