9,322 research outputs found
The 2+2-Signature and the 1+1-Matrix-Brane
We discuss different aspects of the 2+2-signature from the point of view of
the quatl theory. In particular, we compare two alternative approaches to such
a spacetime signature, namely the 1+1-matrix-brane and the 2+2-target spacetime
of a string. This analysis also reveals hidden discrete symmetries of the
2+2-brane action associated with the 2+2-dimensional sector of a
2+10-dimensional target background.Comment: 12 pages, Latex, to appear in Mod. Phys. Lett.
Remarks on Weyl invariant p-branes and Dp-branes
A mechanism to find different Weyl invariant p-branes and Dp-branes actions
is explained. Our procedure clarifies the Weyl invariance for such systems.
Besides, by considering gravity-dilaton effective action in higher dimensions
we also derive a Weyl invariant action for p-branes. We argue that this
derivation provides a geometrical scenario for the Weyl invariance of p-branes.
Our considerations can be extended to the case of super-p-branes.Comment: 18 pages, Late
Some Exceptional Cases in Mathematics: Euler Characteristic, Division Algebras, Cross Vector Product and Fano Matroid
We review remarkable results in several mathematical scenarios, including
graph theory, division algebras, cross product formalism and matroid theory.
Specifically, we mention the following subjects: (1) the Euler relation in
graph theory, and its higher-dimensional generalization, (2) the dimensional
theorem for division algebras and in particular the Hurwitz theorem for normed
division algebras, (3) the vector cross product dimensional possibilities, (4)
some theorems for graphs and matroids. Our main goal is to motivate a possible
research work in these four topics, putting special interest in their possible
links.Comment: 14 pages, Late
Duality, matroids, qubits, twistors and surreal numbers
We show that via the Grassmann-Pl\"ucker relations, the various apparent
unrelated concepts, such as duality, matroids, qubits, twistors and surreal
numbers are, in fact, deeply connected. Moreover, we conjecture the possibility
that these concepts may be considered as underlying mathematical structures in
quantum gravity.Comment: 17 pages, published in Frontier in Physic
Phirotopes, Super p-branes and Qubit Theory
The phirotope is a complex generalization of the concept of chirotope in
oriented matroid theory. Our main goal in this work is to establish a link
between phirotopes, super p-branes and qubit theory. For this purpose we first
discuss maximally supersymmetric solutions of 11-dimensional supergravity from
the point of view of the oriented matroid theory. We also clarify a possible
connection between oriented matroid theory and supersymmetry via the
Grassmann-Pl\"ucker relations. These links are in turn useful for explaining
how our approach can be connected with qubit theory.Comment: Latex, 32 pages, improved versio
Scale-Free Growing Networks and Gravity
We propose a possible relation between complex networks and gravity. Our
guide in our proposal is the power-law distribution of the node degree in
network theory and the information approach to gravity. The established bridge
may allow us to carry geometric mathematical structures, which are considered
in gravitational theories, to probabilistic aspects studied in the framework of
complex networks and vice versa.Comment: Latex, 10 pages, improved versio
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