Related papers: New rigid string instantons in $R^4$
We show how to find explicit expressions for rigid string instantons for general 4-manifold $M$. It appears that they are pseudo-holomorphic curves in the twistor space of $M$. We present explicit formulae for $M=R^4, S^4$. We discuss their…
Generalized Weierstrass formulae for surfaces in four-dimensional space $\Bbb{R}^{4}$ are used to study (anti)self-dual rigid string configurations. It is shown that such configurations are given by superminimal immersions into…
Monopoles and instantons are sheets (membranes) and strings in d=5+1, respectively, and instanton strings can terminate on monopole sheets. We consider a pair of monopole and anti-monopole sheets which is unstable to decay and results in a…
We find new classes of {\it exact} string solutions in a variety of curved backgrounds. They include stationary and dynamical (open, closed, straight, finitely and infinitely long) strings as well as {\it multi-string} solutions, in terms…
We use a recently found method to characterise all the invertible fourth-order difference equations linear in the extremal values based on the existence of a discrete Lagrangian. We also give some result on the integrability properties of…
A self-consistent ansatz is presented for a four-dimensional euclidean solution (instanton) in the vacuum sector of constrained SU(2) Yang-Mills-Higgs theory.
This paper is devoted to the construction of a family of linear sigma models with $(0,4)$ supersymmetry which should flow in the infrared to the stringy version of Yang-Mills instantons on ${\bf R}^4$. The family depends on the full set of…
We say that a system of differential equations d^2x(t)/dt^2=Adx(t)/dt+Bx(t)+Cu(t), in which A and B are m-by-m complex matrices and C is an m-by-n complex matrix, is rigid if it can be reduced by substitutions x(t)=Sy(t),…
Equations which define classical configurations of strings in $R^3$ are presented in a simple form. General properties as well as particular classes of solutions of these equations are considered.
We give the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2d Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
We present two different families of stationary black strings in three dimensions carrying electric and axion charges. Both solutions contain a singular region, which however is quite harmless for string frame geodesic observers, because…
New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are…
We derive the precise relation between level matching condition and fractional instanton numbers in six dimensional, abelian and supersymmetric orbifolds of E8 x E8 heterotic string theory. The fractional part of the two E8 instanton…
Instantons in massless theories do not carry over to massive theories due to Derrick's theorem. This theorem can, however, be circumvented, if a constraint that restricts the scale of the instanton is imposed on the theory. Constrained…
New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…
Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without…
We discuss three classes of solitonic solutions in string theory: instantons, monopoles and string-like solitons. Instantons may provide a nonperturbative understanding of the vacuum structure of string theory, while monopoles may appear in…
We study solutions of the supergravity equations with the string-like sources moving with the speed of light. An exact solution is obtained for the gravitational field of a boosted ring string in any dimension greater than three.
We consider the self-dual Yang-Mills equations in seven dimensions. Modifying the t'Hooft construction of instantons in $d=4$, we find $N$-instanton $7d$ solutions which depend on $8N$ effective parameters and are $E_{6}$-invariant.