Solutions to Yang-Mills equations on four-dimensional de Sitter space

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS$_4$ and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. Slicing dS$_4$ as ${\mathbb R}\times S^3$, via an SU(2)-equivariant ansatz we reduce the Yang-Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a double-well potential. Its local maximum yields a Yang-Mills solution whose color-magnetic field at time $\tau\in{\mathbb R}$ is given by $\tilde{B}_a=-\frac12 I_a/(R^2\cosh^2\!\tau)$, where $I_a$ for $a=1,2,3$ are the SU(2) generators and $R$ is the de Sitter radius. At any moment, this spatially homogeneous configuration has finite energy, but its action is also finite and of the value $-\frac12j(j{+}1)(2j{+}1)\pi^3$ in a spin-$j$ representation. Similarly, the double-well bounce produces a family of homogeneous finite-action electric-magnetic solutions with the same energy. There is a continuum of other solutions whose energy and action extend down to zero.Comment: 1+7 pages; v2: introduction extended, gauge group representation dependence added, minor clarifications, 3 more references; v3: title change, published versio

Dressing Symmetries of Holomorphic BF Theories

We consider holomorphic BF theories, their solutions and symmetries. The equivalence of Cech and Dolbeault descriptions of holomorphic bundles is used to develop a method for calculating hidden (nonlocal) symmetries of holomorphic BF theories. A special cohomological symmetry group and its action on the solution space are described.Comment: 14 pages, LaTeX2

Instantons in six dimensions and twistors

Recently, conformal field theories in six dimensions were discussed from the twistorial point of view. In particular, it was demonstrated that the twistor transform between chiral zero-rest-mass fields and cohomology classes on twistor space can be generalized from four to six dimensions. On the other hand, the possibility of generalizing the correspondence between instanton gauge fields and holomorphic bundles over twistor space is questionable. It was shown by Saemann and Wolf that holomorphic line bundles over the canonical twistor space Tw(X) (defined as a bundle of almost complex structures over the six-dimensional manifold X) correspond to pure-gauge Maxwell potentials, i.e. the twistor transform fails. On the example of X=CP^3 we show that there exists a twistor correspondence between Abelian or non-Abelian Yang-Mills instantons on CP^3 and holomorphic bundles over complex submanifolds of Tw(CP^3), but it is not so efficient as in the four-dimensional case because the twistor transform does not parametrize instantons by unconstrained holomorphic data as it does in four dimensions.Comment: 14 pages; v2: discussion of aims and results extended; v3: published versio

Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons

Due to their explicit construction, Aloff-Wallach spaces are prominent in flux compactifications. They carry G_2-structures and admit the G_2-instanton equations, which are natural BPS equations for Yang-Mills instantons on seven-manifolds and extremize a Chern-Simons-type functional. We consider the Chern-Simons flow between different G_2-instantons on Aloff-Wallach spaces, which is equivalent to Spin(7)-instantons on a cylinder over them. For a general SU(3)-equivariant gauge connection, the generalized instanton equations turn into gradient-flow equations on C^3 x R^2, with a particular cubic superpotential. For the simplest member of the Aloff-Wallach family (with 3-Sasakian structure) we present an explicit instanton solution of tanh-like shape.Comment: 1+17 pages, 1 figur

Instantons on sine-cones over Sasakian manifolds

We investigate instantons on sine-cones over Sasaki-Einstein and 3-Sasakian manifolds. It is shown that these conical Einstein manifolds are K"ahler with torsion (KT) manifolds admitting Hermitian connections with totally antisymmetric torsion. Furthermore, a deformation of the metric on the sine-cone over 3-Sasakian manifolds allows one to introduce a hyper-K"ahler with torsion (HKT) structure. In the large-volume limit these KT and HKT spaces become Calabi-Yau and hyper-K"ahler conifolds, respectively. We construct gauge connections on complex vector bundles over conical KT and HKT manifolds which solve the instanton equations for Yang-Mills fields in higher dimensions.Comment: 1+15 pages, 2 figure

A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation

A bijective map $r: X^2 \longrightarrow X^2$, where $X = \{x_1, ..., x_n \}$ is a finite set, is called a \emph{set-theoretic solution of the Yang-Baxter equation} (YBE) if the braid relation $r_{12}r_{23}r_{12} = r_{23}r_{12}r_{23}$ holds in $X^3.$ A non-degenerate involutive solution $(X,r)$ satisfying $r(xx)=xx$, for all $x \in X$, is called \emph{square-free solution}. There exist close relations between the square-free set-theoretic solutions of YBE, the semigroups of I-type, the semigroups of skew polynomial type, and the Bieberbach groups, as it was first shown in a joint paper with Michel Van den Bergh. In this paper we continue the study of square-free solutions $(X,r)$ and the associated Yang-Baxter algebraic structures -- the semigroup $S(X,r)$, the group $G(X,r)$ and the $k$- algebra $A(k, X,r)$ over a field $k$, generated by $X$ and with quadratic defining relations naturally arising and uniquely determined by $r$. We study the properties of the associated Yang-Baxter structures and prove a conjecture of the present author that the three notions: a square-free solution of (set-theoretic) YBE, a semigroup of I type, and a semigroup of skew-polynomial type, are equivalent. This implies that the Yang-Baxter algebra $A(k, X,r)$ is Poincar\'{e}-Birkhoff-Witt type algebra, with respect to some appropriate ordering of $X$. We conjecture that every square-free solution of YBE is retractable, in the sense of Etingof-Schedler.Comment: 34 page

Self-dual Yang-Mills fields in pseudoeuclidean spaces

The self-duality Yang-Mills equations in pseudoeuclidean spaces of dimensions $d\leq 8$ are investigated. New classes of solutions of the equations are found. Extended solutions to the D=10, N=1 supergravity and super Yang-Mills equations are constructed from these solutions.Comment: 9 pages, LaTeX, no figure

Técnica, princípios e características de avaliação da eficiência econômica da construção e reconstrução de rodovias

Efficiency assessment technique of capital investments in construction and reconstruction of highways is described in this article. Despite the degree of readiness of the methodical device, specialized construction norms of VSN 21-83 focused on implementation of such assessment were not widely adopted in view of the difficulties arising in the course of collecting basic data, their reliability and quality. The present article contains the characteristics of the grouped components and evaluation criteria, in particular, the description of settlement indicators in a section of the intra-transport, extra-transport and social and economic effects resulting from capital investments in linear objects of road infrastructure. On a concrete example the assessment procedure and calculations of summary economic indicators for groups and for the project in general is shown. What shows is a possibility of application of rather difficult technique and its efficiency as scientific tool of complex assessment for the solution of applied tasks in road construction. And use of departmental construction norms in combination with the dynamic methods of assessment based on the analysis of cash flows can increase substantially scientific validity of administrative decisions and quality of investment projects in the field of development of road infrastructure.En este artículo se describe la técnica de evaluación de la eficiencia de las inversiones de capital en la construcción y reconstrucción de carreteras. A pesar del grado de preparación del dispositivo metódico, las normas de construcción especializadas de VSN 21-83 enfocadas en la implementación de dicha evaluación no se adoptaron ampliamente en vista de las dificultades que surgen en el curso de la recopilación de datos básicos, su confiabilidad y calidad. El presente artículo contiene las características de los componentes agrupados y los criterios de evaluación, en particular, la descripción de los indicadores de asentamiento en una sección del transporte interno, transporte extra y los efectos sociales y económicos resultantes de las inversiones de capital en objetos lineales de infraestructura vial. En un ejemplo concreto se muestra el procedimiento de evaluación y los cálculos de indicadores económicos resumidos para grupos y para el proyecto en general. Lo que muestra es una posibilidad de aplicación de una técnica bastante difícil y su eficiencia como herramienta científica de evaluación compleja para la solución de tareas aplicadas en la construcción de carreteras. Y el uso de normas de construcción departamentales en combinación con los métodos dinámicos de evaluación basados en el análisis de flujos de efectivo puede aumentar sustancialmente la validez científica de las decisiones administrativas y la calidad de los proyectos de inversión en el campo del desarrollo de infraestructura vial.A técnica de avaliação de eficiência de investimentos de capital em construção e reconstrução de rodovias é descrita neste artigo. Apesar do grau de prontidão do dispositivo metódico, normas de construção especializadas do VSN 21-83 voltadas para a implementação de tal avaliação não foram amplamente adotadas em vista das dificuldades surgidas no decorrer da coleta de dados básicos, sua confiabilidade e qualidade. O presente artigo contém as características dos componentes agrupados e critérios de avaliação, em particular, a descrição dos indicadores de liquidação em uma seção dos efeitos intra-transporte, extra-transporte e sociais e econômicos resultantes de investimentos de capital em objetos lineares de infraestrutura rodoviária. Em um exemplo concreto, o procedimento de avaliação e os cálculos de indicadores econômicos resumidos para grupos e para o projeto em geral são mostrados. O que mostra é uma possibilidade de aplicação de técnica bastante difícil e sua eficiência como ferramenta científica de avaliação complexa para a solução de tarefas aplicadas na construção de estradas. E o uso de normas de construção departamental em combinação com os métodos dinâmicos de avaliação com base na análise dos fluxos de caixa pode aumentar substancialmente a validade científica das decisões administrativas e da qualidade dos projetos de investimento no campo do desenvolvimento da infraestrutura rodoviária