GRAVITATING (BI-)SPHALERONS

Abstract

The standard model of electroweak interactions is minimally coupled to gravity and the response of the spherically symmetric solutions -the sphaleron and the bisphaleron-to gravity is emphasized. For a given value of the Higgs mass MH , several branches of solutions exist which terminate into cusp-catastrophy at some (MH-depending) critical value of the parameter α defined by the ratio of the vector-boson mass to the Planck mass. A given branch either bifurcates from another one at an intermediate value of α or persists in the limit α → 0 where it terminates into a flat sphaleron or bisphaleron or into a Bartnik-McKinnon solution. These bifurcation patterns are studied in some details.

Domain defects in systems of two real scalar fields

“…In this case the equations of motion do not change but the boundary conditions are now periodic ones, to respect the topology of the circle. The solutions here are like the sphalerons solutions introduced in [17] in the case of a single field -see also [18,19] and references therein for further details. For generality we shall assume that the fields φ and χ are periodic according to…”

Qes Systems, Invariant Spaces and Polynomials Recursions

“…in the construction of the doubly periodic solutions of the Lamé equation [21] (see e.g. [8]) and in the stability analysis of classical solutions available is some low dimensional field theories [22,23,24],.…”

Gravitating sphaleron–antisphaleron systems

“…Rescaling the solutions then shows, that in the limit α → 0 in each case a globally regular EYM solution is reached, corresponding to the first BM solution (n = 1) or a generalized BM solution (n > 1) [10,11]. (Note, that the n = 1 gravitating sphaleron was studied before [7,8,9].) Considering the sets of solutions for different values of n, we note, that with increasing n the maximal value of the coupling constant α max decreases monotonically.…”

“…As for the monopoleantimonopole systems [14], we therefore expect a plethora of gravitating solutions at large scalar coupling. Furthermore, for very large values of the Higgs mass also bisphalerons or 'deformed' sphalerons are present [9,18], which do not exhibit parity reflection symmetry.…”