Related papers: Phirotopes, Super p-branes and Qubit Theory
We considered the possibility that the oriented matroid theory is connected with supersymmetry via the Grassmann-Plucker relations. The main reason for this, is that such relations arise in both in the chirotopes definition of an oriented…
We analyze maximal supersymmetry in eleven-dimensional supergravity from the point of view of the oriented matroid theory. The mathematical key tools in our discussion are the Englert solution and the chirotope concept. We argue that…
We show that qubit and chirotope concepts are closely related. In fact, we prove that the qubit concept leads to a generalization of the chirotope concept, which we call qubitope. Moreover, we argue that a possible qubitope theory may…
We argue that the chirotope concept of oriented matroid theory may be found in different scenarios of physics, including classical mechanics, quantum mechanics, gauge field theory, p-branes formalism, two time physics and Matrix theory. Our…
We establish a connection between oriented matroid theory and loop quantum gravity in (2+2) (two time and two space dimensions) and 8-dimensions. We start by observing that supersymmetry implies that the structure constants of the real…
We claim that $M$(atroid) theory may provide a mathematical framework for an underlying description of $M$-theory. Duality is the key symmetry which motivates our proposal. The definition of an oriented matroid in terms of the Farkas…
A link between matroid theory and $p$-branes is discussed. The Schild type action for $p$-branes and matroid bundle notion provide the two central structures for such a link. We use such a connection to bring the duality concept in matroid…
By combining the concepts of graviton and matroid, we outline a new gravitational theory which we call gravitoid theory. The idea of this theory emerged as an attempt to link the mathematical structure of matroid theory with M-theory. Our…
It is shown that matroid theory may provide a natural mathematical framework for a duality symmetries not only for quantum Yang-Mills physics, but also for M-theory. Our discussion is focused in an action consisting purely of the…
In this work, we consider matroid theory. After presenting three different (but equivalent) definitions of matroids, we mention some of the most important theorems of such theory. In particular, we note that every matroid has a dual matroid…
We review the properties of classical p-brane solutions to supergravity theories, i.e. solutions that may be interpreted as Poincare-invariant hyperplanes in spacetime. Topics covered include the distinction between elementary/electric and…
We give a full classification of the multi-charge supersymmetric $p$-brane solutions in the massless and massive maximal supergravities in dimensions $D\ge2$ obtained from the toroidal reduction of eleven-dimensional supergravity. We derive…
We establish a connection between 4-rebits (real qubits) and the Nambu-Goto action with target `spacetime' of four time and four space dimensions ((4+4)-dimensions)). We motivate the subject with three observations. The first one is that a…
We review a geometrical, so called superembedding, approach to the description of the dynamics of point-like and extended supersymmetric objects (superbranes) in String Theory. The approach is based on a supersymmetric extension of the…
We present f(R) theories of ten-dimensional supergravities, including the fermionic sector up to the quadratic order in fermion fields. They are obtained by performing the conformal scaling on the usual supergravities to the f(R) frame in…
To every realizable oriented matroid there corresponds an arrangement of real hyperplanes. The homeomorphism type of the complexified complement of such an arrangement is completely determined by the oriented matroid. In this paper we study…
This is a review of exceptional field theory: a generalisation of Kaluza-Klein theory that unifies the metric and $p$-form gauge field degrees of freedom of supergravity into a generalised or extended geometry, whose additional coordinates…
We derive p+1-dimensional (p=1,2) maximally supersymmetric U(N) Yang-Mills theory from the wrapped supermembrane on $R^{11-p}\times T^{p}$ in the light-cone gauge by using the matrix regularization. The elements of the matrices in the super…
We investigate the hierarchies of half-supersymmetric branes in maximal supergravity theories. By studying the action of the Weyl group of the U-duality group of maximal supergravities we discover a set of universal algebraic rules…
We discuss the r\^ole of enlarged superspaces in two seemingly different contexts, the structure of the $p$-brane actions and that of the Cremmer-Julia-Scherk eleven-dimensional supergravity. Both provide examples of a common principle: the…