Non-Abelian fields inAdS4spacetime: Axially symmetric, composite configurations

Abstract

We construct new finite energy regular solutions in Einstein-Yang-Mills-SU(2) theory. They are static, axially symmetric and approach at infinity the anti-de Sitter spacetime background. These configurations are characterized by a pair of integers (m, n), where m is related to the polar angle and n to the azimuthal angle, being related to the known flat space monopole-antimonopole chains and vortex rings. Generically, they describe composite configurations with several individual components, possesing a nonzero magnetic charge, even in the absence of a Higgs field. Such Yang-Mills configurations exist already in the probe limit, the AdS geometry supplying the attractive force needed to balance the repulsive force of YangMills gauge interactions. The gravitating solutions are constructed by numerically solving the elliptic Einstein-DeTurck-Yang-Mills equations. The variation of the gravitational coupling constant α reveals the existence of two branches of gravitating solutions which bifurcate at some critical value of α. The lower energy branch connects to the solutions in the global AdS spacetime, while the upper branch is linked to the generalized Bartnik-McKinnon solutions in asymptotically flat spacetime. Also, a spherically symmetric, closed form solution is found as a perturbation around the globally anti-de Sitter vacuum state.

Static black holes with axial symmetry in asymptoticallyAdS4spacetime

“…(A11). This parameter is not fixed a priori, such that YM solutions with a noninteger magnetic charge are allowed [23,34,35].…”

“…The corresponding solitonic solutions have been extensively studied in [23] (and their asymptotically flat counterparts in [31,37]). The most interesting feature found there is the existence for m > 1 of balanced, regular composite configurations, with several distinct components.…”

“…The typical numerical error for the solutions reported in this work is estimated to be of the order of 10 −4 , with smaller values for the norm of the ξ field. Further details on the numerical scheme can be found in [23].…”

“…At infinity, the gauge potentials are required to satisfy a set of boundary conditions originally proposed in [23]. The data there contain a new positive integer, m, which is interpreted as a polar winding number solution.…”

Gauge fields, nonlinear realizations, supersymmetry

“…These include the twistor approach to strings and particles (see, e.g., [184,185]), the studies related to the AGT (Alday-Gaiotto-Tachikawa) conjecture (see, e.g., [186]) and, more recently, the explicit construction of instantons and monopoles (see, e.g., [187]). In view of lacking of space, I will not dwell on these issues.…”