Features of gravity–Yang-Mills hierarchies inddimensions

Abstract

Higher dimensional, direct analogues of the usual d = 4 Einstein-Yang-Mills (EYM) systems are studied. These consist of the gravitational and Yang-Mills hierarchies in d = 4p dimensional spacetimes, both consisting of 2p-form curvature terms only. Regular and black hole solutions are constructed in 2p + 2 ≤ d ≤ 4p, in which dimensions the total mass-energy is finite, generalising the familiar BartnikMcKinnon solutions in EYM theory for p = 1. In d = 4p, this similarity is complete. In the special case of d = 2p + 1, just beyond the finite energy range of d, exact solutions in closed form are found. Finally, d = 2p + 1 purely gravitational systems, whose solutions generalise the static d = 3 BTZ solutions, are discussed.

Gravitating BPS monopoles in all d = 4 p spacetime dimensions

“…This would result in the dilution of the analogy with the latter at least on the quantitative level. This choice was made previously in the study of the EYM systems in 4p dimensional spacetimes in [26], where it resulted in the tight similarity in the qualitative properties of the solutions of the p−th YM system gravitated with the p(= q)−th Einstein systems in all 4p dimensions.…”

“…and indeed in [26] the EYM system has been studied for all values in this range. The presence of the Higgs field, however, requires d = 4p.…”

“…The first alternative describes a YMH system in a fixed gravitational background, either flat (no gravity) or a Schwarzschild type black hole. The second alternative describes the (self gravitating) EYM system of [26].…”

“…Suitably defined EYM systems featuring higher order YM curvature 1 terms in all d = D + 1 spacetime dimensions were studied in [11,12] without cosmological constant, and in [13,14] with cosmological constant. These latter differ from their d = 3+1 dimensional EYM analogues [4,6], which are unstable (sphaleronic) and have no gravity decoupling limits, in that some of them do have gravity decoupling limits which are stabilised by Chern-Pontryagin (instantonic) charges.…”

Black holes and gravitating axially symmetric non-abelian solitons in d = 3+1 and d = 4+1

“…In is known such terms are necessary to ensure that the solution yields a finite mass [9,10,12,13,15,14]. The physical justification for introducing higher order YM terms is that these occur in the low energy effective action of string theory [29].…”