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 configuration as a stable fixed point of the flow in the large flow time. Applying the method to the $SU(2)$-Higgs model (the Weinberg angle $θ_W$ is $0$) in four dimensions, we obtain the sphaleron configuration whose energy coincides with previous studies numerically. We can also show that the Chern-Simons number of the solution has a half-integer.
The topology of configuration space may be responsible in part for the existence of sphalerons. Here, sphalerons are defined to be static but unstable finite-energy solutions of the classical field equations. Another manifestation of the nontrivial topology of configuration space is the phenomenon of spectral flow for the eigenvalues of the Dirac Hamiltonian. The spectral flow, in turn, is related to the possible existence of anomalies. In this review, the interconnection of these topics is illustrated for three particular sphalerons of SU(2) Yang-Mills-Higgs theory.
We show that unstable D-branes play the role of ``D-sphalerons'' in string theory. Their existence implies that the configuration space of Type II string theory has a complicated homotopy structure, similar to that of an infinite Grassmannian. In particular, the configuration space of Type IIA (IIB) string theory on $\R^{10}$ has non-trivial homotopy groups $π_k$ for all $k$ even (odd).
We perform a systematic study of stationary sphaleron-antisphaleron systems of Weinberg-Salam theory at the physical value of the weak mixing angle. These systems include rotating sphaleron-antisphaleron pairs, chains and vortex rings. We show that the angular momentum of these solutions is proportional to their electric charge. We study the dependence of their energy and magnetic moment on their angular momentum. We also investigate the influence of their angular momentum on their local properties, in particular on their energy density and on the node structure of their Higgs field configurat…
We perform analytic construction of a sphaleron-like solution in the 4-dimensional (4D) space-time invoking the framework of 5D SU(2) gauge theory. By the sphaleron-like solution we mean a static finite energy solution to the equation of motion, which carries the Chern-Simons number $N_\text{CS}=\frac{1}{2}$. Since we are interested in the static solution in the low-energy effective theory, we focus on the part of the action which contains only the gauge fields in the 4D space (not space-time), $(A_{i}, A_{y}) (i = 1,2,3)$ and keep only the Kaluza-Klein zero modes of these fields. Interestingl…
We study the spectrum of the Dirac Hamiltonian in the presence of high temperature sphaleron-like fluctuations of the electroweak gauge and Higgs fields, relevant for the conditions prevailing in the early universe. The fluctuations are created by numerical lattice simulations. It is shown that a change in Chern-Simons number by one unit is accompanied by eigenvalues crossing zero and a change of sign of the generalized chirality $\tGf= (-1)^{2T+1} \gf$ which labels these modes. This provides further evidence that the sphaleron-like configurations observed in lattice simulations may be viewed …
In an external magnetic field, the energy of the electroweak sphaleron---representing the energy barrier to baryon and lepton number violation---decreases but remains nonzero until the upper Ambjorn-Olesen critical field strength set by the Higgs mass and the electric charge, where it vanishes. We demonstrate this by numerically computing the sphaleron configuration in the presence of an external magnetic field, over the full range of field strengths until the energy barrier vanishes. We discuss the implications for baryogenesis in the early universe, and the possibility of observing of baryon…
Nonlinear electroweak sphaleron clouds around Kerr black holes
Universidade de Aveiro（阿威罗大学）；Centre for Research and Development in Mathematics and Applications (CIDMA)（数学与应用数学研究与发展中心）；Universität Oldenburg（奥尔登堡大学）；U. Federal do Pará（帕拉联邦大学）
3D electroweak sphalerons on the lattice are used as test configurations for definitions of various topological defects. In the maximally Abelian gauge they are shown to contain a symmetric array of Abelian monopoles and anti-monopoles connected by two kinds of Abelian vortex strings. Gauge-invariant lattice definitions of the Nambu monopole and the Z-vortex string are formulated which correspond to Abelian projection from the unitary gauge. The sphalerons contain in their core just one (non-Abelian) Nambu monopole-anti-monopole pair (connected by a Z-string) in an unstable saddle point bound …
Type I string theory can be dimensionally reduced on group manifolds. The compactification on $S^3\times S^3$ leads to the N=4 gauged SU(2)$\times$SU(2) supergravity in four dimensions, which admits the BPS monopole type non-Abelian vacuum. The reduction on $S^3\times AdS_3$ gives the Euclidean N=4 gauged SU(2)$\times$SU(1,1) supergravity admitting a globally regular supersymmetric non-Abelian background. The latter can be analytically continued to the Lorentzian sector, which gives the regular, unstable particle-like configuration known as gravitational sphaleron. When lifted to D=10, the Euc…
The space of static finite-energy configurations in the electroweak theory admits a $Z_2$ topological structure. More precisely, we show that this space contains two disconnected sectors of unstable gauge-Higgs fields odd under a properly defined generalized parity. This classification extends the description of baryon and lepton number violating electroweak processes to the symmetric phase of the theory. Configurations with odd pure-gauge behaviour at spatial infinity, such as the sphaleron, multisphalerons, electroweak strings as well as an infinite surface of their equivalents, have half-in…
Spectral flow of chiral fermions in the background of electroweak sphalerons is studied. A fermion field configuration that interpolates between the sphaleron zero mode and the asymptotic fermion modes is proposed for the level crossing left handed fermion fields. It is shown that the fermionic electromagnetic currents with non-trivial helicity are produced during the level crossing. Cosmic magnetic field generation due to these currents is briefly discussed.
We propose a new alternative for baryogenesis which resolves a number of the problems associated with GUT and electroweak scenarios, and which may allow baryogenesis even in modest extensions of the standard model. If the universe never reheats above the electroweak scale following inflation, GUT baryon production does not occur and at the same time thermal sphalerons, gravitinos and monopoles are not produced in abundance. Nevertheless, non-thermal production of sphaleron configurations via preheating could generate the observed baryon asymmetry of the universe.
Euclidean field theory on 4-dimensional sphere is suggested for the study of high energy multiparticle production. The singular classical field configurations are found in scalar and SU(2)-gauge theories and the cross section of 2->n processes is calculated. It is shown,that the cross section has a maximum at the energy compared to the sphaleron mass.
We explore the Higgs-Gauge configuration space in the standard electroweak theory. We outline a general prescription that uses the non-trivial topology associated with the gauge group of the theory, to find known solutions of the Euclidean classical equations of motion and motivate the existence of novel ones. In Minkowski spacetime we present evidence for the existence of approximate breathers -- long-lived, spatially localized, temporally periodic configurations. We consider heavy fermion quantum fluctuations about static Higgs-Gauge configurations, and argue for the existence of stable ferm…
The relation between connections on 2-dimensional manifolds and holomorphic bundles provides a new perspective on the role of classical gauge fields in quantum field theory in two, three and four dimensions. In particular we show that there is a close relation between unstable bundles and monopoles, sphalerons and instantons. Some of these classical configurations emerge as nodes of quantum vacuum states in non-confining phases of \qft which suggests a relevant role for those configurations in the mechanism of quark confinement in QCD.
A pure Yang-Mills theory extended by addition of a quartic term is considered in order to study the transition from the quantum tunneling regime to that of classical, i.e. thermal, behaviour. The periodic field configurations are found, which interpolate between the vacuum and sphaleron field configurations. It is shown by explicit calculation that only smooth second order transitions occur for all permissible values of the parameter $Ł$ introduced with the quartic term. The theory is one of the rare cases which can be handled analytically.
We construct the multi-charge generalizations for the electroweak magnetic monopole solution of Cho and Maison within a wide range of values of the magnetic charge. We use the same ansatz for the axially symmetric fields as the one previously employed to construct the electroweak sphalerons and compare the internal structure of monopoles with that of sphalerons. The monopoles have zero dipole moment but a finite quadrupole momentum that rapidly increases with growing magnetic charge. For large charges, the monopole configurations are strongly squashed and show inside a bubble of symmetric phas…
Particle physics has for some time made extensive use of extended field configuations such as solitons, instantons, and sphalerons. However, no direct use has yet been made of the quite extensive literature on ``localized wave'' configurations developed by the engineering, optics, and mathematics communities. In this article I will exhibit a particularly simple ``physical wavelet'' -- it is a Lorentz covariant classical field configuration that lives in physical Minkowski space. The field is everwhere finite and nonsingular, and has quadratic falloff in both space and time. The total energy is…
Within SU(2) Higgs-Proca theory, we obtain a family of nontopological static solutions describing localized, finite-energy configurations (Proca balls). The gauge symmetry of the theory is explicitly broken by introducing a vector Proca field whose components have different masses. Such solutions describe particlelike systems,the crucial feature of which is that they either possess a nonzero total angular momentum or have a flux of electric field through the plane of symmetry of such objects. It is shown that the angular momentum is provided by static crossed electric and magnetic fields. The …
We show that dyon and magnetic monopole can be constructed in the gauge-independent way for the $SU(2)$ Yang--Mills theory even in the absence of the scalar field. This result is derived from the recent proposal for obtaining non-trivial topological configurations responsible for quark confinement in the Yang-Mills theory based on the Confinement-Higgs complementary relationship between the pure Yang-Mills theory and the gauge-scalar model with an adjoint scalar field of the fixed length. We discuss how such configurations have the implications for quark confinement.
In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is to modify the Lebesgue measure of configuration space of many particles by adding singular measures over the subspaces of configuration space in which the positions of two or more particles coincide.
In this master thesis a configuration space method presented by C. Dullemond and E. van Beveren for computing all propagators of a scalar field (Wightman, Hadamard and Schwinger functions,retarded, advanced and Feynman propagator) is reviewed for four-dimensional Minkowski and Anti de Sitter spacetime AdS_4. This method is then applied for AdS_d as well as de Sitter spacetime dS_d of arbitrary dimension d, obtaining results in agreement with the literature. The advantages of the method are that it needs neither mode summation nor analytic continuation from euclidean time, while delivering the …
Brane world six dimensional scenarios with string like metric has been proposed to alleviate the problem of field localization. However, these models have been suffering from some drawbacks related with energy conditions as well as from difficulties to find analytical solutions. In this work, we propose a model where a brane is made of a scalar field with bounce-type configurations and embedded in a bulk with a string-like metric. This model produces a sound AdS scenario where none of the important physical quantities is infinite. Among these quantities are the components of the energy momentu…
We classify almost all classical string configurations, considered in the framework of the semi-classical limit of the string/gauge theory duality. Then, we describe a procedure for obtaining the conserved quantities and the exact classical string solutions in general string theory backgrounds, when the string embedding coordinates depend non-linearly on the worldsheet time parameter.
We study the effective actions of various brane configurations in Matrix theory. Starting from the 0+1 dimensional quantum mechanics, we replace coordinate matrices by covariant derivatives in the large N limit, thereby obtaining effective field theories on the brane world volumes. Even for noncompact branes, these effective theories are of Yang-Mills type, with constant background magnetic fields. In the case of a D2-brane, we show explicitly how the effective action equals the large magnetic field limit of the Born-Infeld action, and thus derive from Matrix theory the action used by Polchins…
