Regularity of static axially symmetric solutions inSU(2)Yang-Mills-dilaton theory

Abstract

The regularity of static axially symmetric solutions in SU (2) Yang-Mills-dilaton theory is examined. We show that the solutions obtained previously within a singular Ansatz for the non-abelian gauge field can be gauge transformed into a regular form. The local form of the gauge transformation is given on the singular axis and at the origin.PACS number(s): 11.15.Kc

Spinning electroweak sphalerons

“…Transforming (10) to Cartesian coordinates one requires that all term proportional to 1= and 1=r should vanish at the z axis and at the origin, respectively. At least for n ¼ AE1 no additional complications at the axis then arise [11] and the fields (10) are everywhere regular. These boundary conditions still allow for a residual gauge freedom (5) with vanishing for ¼ 0, for z ¼ 0, and for r ¼ 1.…”

Monopole-antimonopole solution of the SU(2) Yang-Mills-Higgs model

“…The Ansatz is not a priori well defined on the z-axis and at the origin. However, for solutions of the field equations, we have performed an expansion of the gauge and Higgs field functions near the z-axis and near the origin [18]. Inserting these expansions into the Ansatz we find that the gauge potential and the Higgs field are well defined and (at least) twice differentiable on the z-axis and at the origin.…”

Static axially symmetric Einstein-Yang-Mills-dilaton solutions: Addendum—asymptotic solutions

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gr-qc/9909160Recently, we have constructed static axially symmetric regular and black hole solutions in SU(2) Einstein-Yang-Mills (EYM) and Einstein-Yang-Mills-dilaton (EYMD) theory [1][2][3][4][5][6]. Representing generalizations of the spherically symmetric regular and black hole solutions [7][8][9]6], these solutions are characterized by two integers, their winding number n and the node number k of their gauge field functions.

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