Multi-instantons in R-4 and minimal surfaces in R-2,R-1

2000-08-01
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 that topological number, instanton moduli space and anti-self-dual solutions have representations in terms of minimal surfaces. The issue of topological charge is quite subtle because the surfaces that appear are non compact. This minimal surface/instanton correspondence allows us to define a metric on the configuration space of the gauge fields. We obtain the minimal surface representation of an instanton with arbitrary charge. The trivial vacuum and the BPST instanton as minimal surfaces are worked out in detail. BPS monopoles and the geodesics are also discussed.
JOURNAL OF HIGH ENERGY PHYSICS

Suggestions

Scalar waves in spacetimes with closed timelike curves
Buğdaycı, Necmi; Başkal, Sibel; Department of Physics (2005)
The existence and -if exists- the nature of the solutions of the scalar wave equation in spacetimes with closed timelike curves are investigated. The general properties of the solutions on some class of spacetimes are obtained. Global monochromatic solutions of the scalar wave equation are obtained in flat wormholes of dimensions 2+1 and 3+1. The solutions are in the form of infinite series involving cylindirical and spherical wave functions and they are elucidated by the multiple scattering method. Explici...
Spatial synthesis by disjunctive constraint satisfaction
Baykan, CA; Fox, MS (Cambridge University Press (CUP), 1997-09-01)
The spatial synthesis problem addressed in this paper is the configuration of rectangles in 2D space, where the sides of the rectangles are parallel to an orthogonal coordinate system. Variables are the locations of the edges of the rectangles and their orientations. Algebraic constraints on these variables define a layout and constitute a constraint satisfaction problem. We give a new O(n(2)) algorithm for incremental path-consistency, which is applied after adding each algebraic constraint. Problem requir...
Finite rigid sets in curve complexes of non-orientable surfaces
Ilbıra, Sabahattin; Korkmaz, Mustafa; Department of Mathematics (2017)
A finite rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map defined on this subcomplex into the curve complex is induced from an automorphism of curve complex. In this thesisi we find finite rigid sets in the curve complexes of connected, non-orientable surfaces of genus g with n holes, where g+n neq 4. 
Least-squares finite element solution of Euler equations with adaptive mesh refinement
Akargün, Hayri Yiğit; Sert, Cüneyt; Department of Mechanical Engineering (2012)
Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the me...
Singular potentials and moving boundaries in 3D
Yuce, C (Elsevier BV, 2004-02-16)
In this Letter, the problem of a spinless particle under the time-dependent harmonic oscillator potential and a singular potential with a moving boundary is studied in the spherical coordinates. Some transformations are used to transform the moving boundary conditions to the fixed boundary conditions. An exact solution is constructed.
Citation Formats
B. Tekin, “Multi-instantons in R-4 and minimal surfaces in R-2,R-1,” JOURNAL OF HIGH ENERGY PHYSICS, pp. 0–0, 2000, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54782.