相关论文: Algebraic Geometry Approach in Theories with Extra…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
Universal algebraic geometry allows considering of geometric properties of every universal algebra. When two algebras have same algebraic geometry? We must consider the categories of algebraic closed sets of these algebras to answer this…
The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem due…
Recently by us was proposed the model where Einstein's equation on the brane was connected with Maxwell's multi-dimensional equations in pseudo-Euclidean space. Based on this idea unification of 4-dimensional gravity and electromagnetism in…
The purpose of this paper is to provide a new account of multiplicity for finite morphisms between smooth projective varieties. Traditionally, this has been defined using commutative algebra in terms of the length of integral ring…
In this review we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is…
We consider stochastic versions of Euler--Arnold equations using the infinite-dimensional geometric approach as pioneered by Ebin and Marsden. For the Euler equation on a compact manifold (possibly with smooth boundary) we establish local…
In this thesis quadratic and cubic algebras, which are extensions of SU(1,1) and SU(2) are studied in detail, with particular attention being given to their construction, their finite and infinite dimensional irreducible representations and…
The algebraic geometry of a universal algebra $\mathbf{A}$ is defined as the collection of solution sets of term equations. Two algebras $\mathbf{A}_1$ and $\mathbf{A}_2$ are called algebraically equivalent if they have the same algebraic…
We present new rotating black brane solutions which solve Einstein's equations with cosmological constant $\Lambda$ in arbitrary dimension $d$. For negative $\Lambda$, the branes naturally appear in AdS supergravity compactifications, and…
We derive a gravitational block formula for the supersymmetric action for a general class of supersymmetric AdS solutions, described by GK geometry. Extremal points of this action describe supersymmetric AdS$_3$ solutions of type IIB…
Models predicting the existence of extra spatial dimensions offer compelling and novel solutions to outstanding problems of the Standard Model. In such models, our universe exists on a 4 dimensional brane embedded in a larger dimensional…
In black hole physics, inflationary cosmology, and quantum field theories, it is conjectured that the physical laws are subject to radical changes below the Planck length. Such changes are due to effects of quantum gravity believed to…
We investigate the geometrical properties of static vacuum $p$-brane solutions of Einstein gravity in $D=n+p+3$ dimensions, which have spherical symmetry of $S^{n+1}$ orthogonal to the $p$-directions and are invariant under the translation…
We present several new examples of nontrivial 4d N=1 superconformal field theories. Some of these theories exhibit exotic global symmetries, including non-simply laced groups (such as $F_4$). They are obtained by studying threebrane probes…
Starting from the most general second-order in derivatives theories describing extended objects of arbitrary dimension evolving geodetically in a codimension-one flat ambient space-time, we determine the subset of models yielding…
Holographic modeling of strongly correlated many-body systems motivates the study of novel spacetime geometries where the scaling behavior of quantum critical systems is encoded into spacetime symmetries. Einstein-Dilaton-Maxwell theory has…
It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above…
We present a scheme of biquaternionic algebrodymamics based on a nonlinear generalization of the Cauchy-Riemann holomorphy conditions considered therein as fundamental field equations. The automorphism group SO(3,C) of the biquaternion…
We derive static spherically symmetric regular black holes as vacuum solutions to purely gravitational theories in four dimensions. To that end, we construct four-dimensional non-polynomial gravities starting from subclasses of…