Related papers: Sphalerons, spectral flow, and anomalies
The topological structure of field theory often makes inevitable the existence of stable and unstable localised solutions of the field equations. These are minima and saddle points of the energy. Saddle point solutions occurring this way…
We consider pure $SU(2)$ Yang-Mills theory when the space is compactified to a 3-dimensional sphere with finite radius. The Euclidean classical self-dual solutions of the equations of motion (the instantons) and the static finite energy…
Cosmological solutions with a homogeneous Yang-Mills field which oscillates and passes between topologically distinct vacua are discussed. These solutions are used to model the collapsing Bartnik-McKinnon gravitational sphaleron and the…
We prove the instability of the gravitating regular sphaleron solutions of the $SU(2)$ Einstein-Yang-Mills-Higgs system with a Higgs doublet, by studying the frequency spectrum of a class of radial perturbations. With the help of a…
We propose a formalism to obtain the electroweak sphaleron, which is one of the static classical solutions, using the gradient flow method. By adding a modification term to the gradient flow equation, we can obtain the sphaleron…
The spectral flow is ubiquitous in the physics of soliton-fermion interacting systems. We study the spectral flows related to a continuous deformation of background soliton solutions, which enable us to develop insight into the emergence of…
We construct sphaleron solutions with discrete symmetries in Yang-Mills-Higgs theory coupled to a dilaton. Related to rational maps of degree N, these platonic sphalerons can be assigned a Chern-Simons number Q=N/2. We present sphaleron…
Solutions to the Yang-Mills field equations which describe exploding or imploding shells of gauge field and which may serve as approximations to the exploding sphaleron are discussed. The solutions are conformally related to $SO(2)\times…
A one-parameter family of nonlinear (quartic) Klein-Gordon models having a sphaleron solution is studied. The sphaleron arises from a saddle point between true and false vacua in the energy functional. Its instability is shown be governed…
Sphalerons -- unstable static solutions of classical field equations in (d+1)-dimensional space-time -- may be viewed as euclidean solutions in d dimensions. We discuss their role in the large order asymptotics of the perturbation theory.…
Subject of this talk is an overview of results on self-gravitating solitons of the classical Yang-Mills-Higgs theory. One finds essentially two classes of solitons, one of them corresponding to the magnetic monopoles the other one to the…
We define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This $G$-equivariant spectral flow shares…
Motivated by the Kaluza-Klein theory with a large number of extra spacetime dimensions, we present a numerical study of static, spherically symmetric sphaleron solutions coupled to the dilaton fields. We show that sphalerons may have…
We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills-dilaton theory. This sequence is parametrized by the number $n$ of zeros of a component of the gauge field…
Static spherically symmetric asymptotically flat particle-like and black hole solutions are constructed within the SU(2) sector of 4-dimensional heterotic string effective action. They separate topologically distinct Yang-Mills vacua and…
Real-time anomalous fermion number violation is investigated for massless chiral fermions in spherically symmetric SU(2) Yang-Mills gauge field backgrounds which can be weakly dissipative or even nondissipative. Restricting consideration to…
After the discovery of the Higgs boson and the rather precise measurement of all electroweak boson's masses the local structure of the electroweak symmetry breaking potential is already quite well established. However, despite being a key…
We show that the cosmological sphaleron of Einstein-Yang-Mills system can be produced from real tunneling geometries. The sphaleron will tend to roll down to the vacuum or pure gauge field configuration, when the universe evolves in the…
We prove a spectral flow formula for one-parameter families of Hamiltonian systems under homoclinic boundary conditions, which relates the spectral flow to the relative Maslov index of a pair of curves of Lagrangians induced by the stable…
The computations of solutions of the field equations in the Model of Topological Particles, formulated with a scalar SU(2)-field, have shown instabilities leading to discrepancies between the numerical and analytical solutions. We identify…