Related papers: More on Membranes in Matrix Theory
We present a construction in Matrix theory of longitudinal 5-branes whose geometry in transverse space corresponds to a 4-sphere. We describe these branes through an explicit construction in terms of N*N matrices for a particular infinite…
In this paper we derive some new invariant solutions of Einstein-Maxwell's field equations for string fluid as source of matter in cylindrically symmetric space-time with Variable Magnetic Permeability. We also discuss the physical and…
We consider the matrix model associated with pp-wave background and construct supersymmetric branes. In addition to the spherical membrane preserving 16 supersymmetries, one may construct rotating elliptic membranes preserving 8…
For real projective spaces, (a) the Euclidean immersion dimension, (b) the existence of axial maps, and (c) the topological complexity are known to be three facets of the same problem. But when it comes to embedding dimension, the classical…
Given a space X we study the topology of the space of embeddings of X into $\mathbb{R}^d$ through the combinatorics of triangulations of X. We give a simple combinatorial formula for upper bounds for the largest dimension of a sphere that…
For the SU(N) invariant supersymmetric matrix model related to membranes in 11 space-time dimensions, the general (bosonic) solution to the equations $Q_\beta^\dagger \Psi =0$ ($Q_\beta \Psi=0$) is determined.
The paper deals with the static spherically symmetric wormhole solutions in $f(R)$-modified gravity theory with anisotropic matter field and for some particular choices for the shape functions. The present work may be considered as an…
We present a wormhole solution in four dimensions. It is a solution of an Einstein Maxwell theory plus charged massless fermions. The fermions give rise to a negative Casimir-like energy, which makes the wormhole possible. It is a long…
In a polydiagonal subspace of the Euclidean space, certain components of the vectors are equal (synchrony) or opposite (anti-synchrony). Polydiagonal subspaces invariant under a matrix have many applications in graph theory and dynamical…
We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds. The main subjects are as follows: (1)Location of the essential spectrum. (2)Absence of eigenvalues embedded in the continuous spectrum. (3)Limiting…
In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…
An invariant of orientable 3-manifolds is defined by taking the minimum $n$ such that a given 3-manifold embeds in the connected sum of $n$ copies of $S^2 \times S^2$, and we call this $n$ the embedding number of the 3-manifold. We give…
We aim at finding static, spherically symmetric, vacuum solutions of a gauge invariant theory of gravity over Weyl integrable geometry spaces. It arises that vacuum wormholes of pure geometric nature are solutions of this theory. This means…
An n-dimensional analogue of the Klein bottle arose in our study of topological complexity of planar polygon spaces. We determine its integral cohomology algebra and stable homotopy type, and give an explicit immersion and embedding in…
By analysing supersymmetry transformations we derive new BPS equations for the D=11 fivebrane propagating in flat space that involve the world-volume three-form. The equations generalise those of 2,3,4 and 5 dimensional special Lagrangian…
We consider non-chiral symmetry-protected topological phases of matter in two spatial dimensions protected by a discrete symmetry such as $\mathbb{Z}_K$ or $\mathbb Z_K \times \mathbb Z_K $ symmetry. We argue that modular…
Inversive geometry can be used to generate exactly self-similar space-filling sphere packings. We present a construction method in two dimensions and generalize it to search for packings in higher dimensions. We newly discover 29…
Examples of stable, non-BPS M-theory membrane configuration are constructed via M(atrix) theory. The stable membranes are localized on O4 or O8 orientifolds, which projects Chan-Paton gauge bundle of M(atrix) zero-brane partons to USp-type.…
We show that every entire solution to the Bernoulli (or one-phase) free boundary problem with finite Morse index in $\mathbb{R}^3$ is axially symmetric. In fact, we additionally prove that the same result would follow in any dimension $4…
We explicitly construct soliton solutions in the low energy description of M-theory on S^1/Z_2. It is shown that the 11-dimensional membrane is a BPS solution of this theory if stretched between the Z_2 hyperplanes. A similar statement…