General relativistic analogue solutions for the Yang-Mills theory

Abstract

Finding solutions to non-linear field theories, such as Yang-Mills theories or general relativity, is usually difficult. The field equations of Yang-Mills theories and general relativity are known to share some mathematical similarities, and this connection can be used to find solutions to one theory using known solutions of the other theory. For example, the Schwarzschild solution of general relativity can be shown to have a mathematically similar counterpart in Yang-Mills theory. In this article we will discuss several solutions to the Yang-Mills equations which can be found using this connection between general relativity and Yang-Mills theory. Some comments about the possible physical meaning of these solutions will be discussed. In particular it will be argued that some of these analog solutions of Yang-Mills theory may have some connection with the confinement phenomenon. To this end we will briefly look at the motion of test particles moving in the background potential of the Schwarzschild analog solution. * For the memorial issue of Theo. Math. Phys. in memory of F.A. Lunev

Singular Soliton Solution in the Chern–simons–cp(1) Model

“…[11] the authors considered the hole plane and showed that there are no solutions besides the trivial one, here we prove that excluding the origin of the plane it is possible to find a non trivial solution. It is, also, interesting to comment that similar solution for Yang-Mills-Higgs theory in (3+1) dimensions were found in references [16]- [17]- [18].…”

Exact solutions for the biadjoint scalar field

“…[53], as well as the extended Yang-Mills solutions of refs. [48,49,54]. In the present case, substituting eq.…”

Perturbative Quantum Gravity and its Relation to Gauge Theory

“…The Maldacena conjecture [94, 2], for example, relates the weak coupling limit of a gravity theory on an anti-de Sitter backround to a strong coupling limit of a special supersymmetric gauge field theory. There is also a long history of papers noting that gravity can be expressed as a gauging of Lorentz symmetry [135, 82, 78], as well as examples of non-trivial similarities between classical solutions of gravity and non-Abelian gauge theo ries [126]. In this review a different, but very general, relationship between the weak coupling limits of both gravity and gauge theories will be described.…”