Related papers: Non-Collapsing Membrane Instantons in Higher Dimen…
By considering 5--dimensional cosmological models with a bulk filled with a pressureless scalar field; equivalently dust matter, and a negative cosmological constant, we have found a regular instantonic solution which is free from any…
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
We study the standard angular momentum algebra $[x_i,x_j]=i\lambda \epsilon_{ijk}x_k$ as a noncommutative manifold $R^3_\lambda$. We show that there is a natural 4D differential calculus and obtain its cohomology and Hodge * operator. We…
It was recently found that the Lee-Huang-Yang (LHY) correction to the mean-field Hamiltonian suppresses the collapse and creates stable localized modes (two-component "quantum droplets", QDs) in two and three dimensions. We construct…
We use the bailout embeddings of three-dimensional volume-preserving maps to study qualitatively the dy- namics of small spherical neutrally buoyant impurities suspended in a time-periodic incompressible fluid flow. The accumulation of…
We consider anisotropic cosmological models with an universe of dimension 4 or more, factorized into n>1 Ricci-flat spaces, containing an m-component perfect fluid of m non-interacting homogeneous minimally coupled scalar fields under…
It is shown that a gauged nonlinear $O(3)$ sigma model with anomalous magnetic moment interaction in $2+1$ dimensions is exactly integrable for static, self-dual field configurations. The matter fields are exactly equivalent to those of the…
We find new obstructions on the topology of monotone Lagrangian submanifolds of $C^{n}$ under some hypothesis on the homology of their universal cover. In particular we show that nontrivial connected sums of manifolds of odd dimensions do…
Some instanton corrections to the universal hypermultiplet moduli space metric of the type-IIA string theory compactified on a Calabi-Yau threefold arise due to multiple wrapping of BPS membranes and fivebranes around certain cycles of…
Important models for immortal solutions of Ricci flow that collapse with bounded curvature come from locally G-invariant solutions on principal bundles, where G is a nilpotent Lie group. In this paper, we establish convergence and…
We obtain numerical solutions for rotating topological solitons of the nonlinear $\sigma$-model in three-dimensional Anti-de Sitter space. Two types of solutions, $i)$ and $ii)$, are found. The $\sigma$-model fields are everywhere well…
We consider the motion of incompressible viscous non-homogeneous fluid described by the Navier-Stokes equations in a bounded cylinder under boundary slip conditions. Assume that the third co-ordinate axis is the axis of the cylinder.…
We discuss non-perturbative effects in the ABJM model due to monopole instantons. We begin by constructing the instanton solutions in the $U(2)\times U(2)$ model, explicitly, and computing the Euclidean action. The Wick-rotated Lagrangian…
We study invariant manifolds of measure-valued solutions of the partial differential equation for geodesic flow of a pressureless fluid. These solutions describe interaction dynamics on lower-dimensional support sets; for example, curves,…
Some models providing shell-shaped static solutions with compact support (compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. These solutions turn out to be topological…
It is known that self-duality equations for multi-instantons on a line in four dimensions are equivalent to minimal surface equations in three dimensional Minkowski space. We extend this equivalence beyond the equations of motion and show…
Quantum non-perturbative geometry of the universal hypermultiplet is investigated. We consider the simple case when the D-instantons, originating from the Calabi-Yau wrapped D2-branes, preserve a U(1)xU(1) symmetry of the universal…
In theories where spacetime is a direct product of Minkowski space ($M^4$) and a d dimensional compact space ($K^d$), there can exist topological solitons that simultaneously wind around $R^3$ (or $R^2$ or $R^1$) in $M^4$ and the compact…
With a 4-form ansatz of 11-dimensional supergravity over non-dynamical AdS$_4 \times S^7/Z_k$ background, with the internal space as a $S^1$ Hopf fibration on CP$^3$, we get a consistent truncation. The (pseudo)scalars, in the resulting…
We present a quantum mechanical model of spherical supermembranes. Using superfields to represent the cartesian coordinates of the membrane, we are able to exactly determine its supersymmetric vacua. We find there are two classical vacua,…