Gauge fields with vanishing scalar invariants

Abstract

We consider extension of some established techniques of study of tensor fields on Lorentzian manifolds of arbitrary dimension to non-Abelian gauge covariant fields. These are then applied to study of gauge fields with vanishing scalar curvature invariants and universal Yang-Mills fields, for which all possible higher-order corrections to the Yang-Mills equation identically vanish.

Einstein-Yang-Mills fields immune to quantum corrections

“…Now that theoretical setting for generalizations of EYM theories is established, we can discuss conditions under which the individual types of corrections associated with L HC vanish and thus complete discussion started in [10], where only corrections ∼ δS A /δA µ to the Yang-Mills equation for test gauge fields were considered.…”

“…In particular, F is a null field strength living in a degenerate Kundt spacetime g and propagates along a geodetic null vector ℓ with zero shear, twist and divergence [10]. By the same token, the requirement of vanishing gravitational corrections δS g /δg µν constricts g to be V SI [9].…”

“…Aforementioned works on universal spacetimes and electromagnetic fields subsequently enabled a complete characterization of Einstein-Maxwell fields immune to any higher-order corrections [9] and initiated effort to investigate situation in the territory of nonabelian gauge fields. 2 First steps in a more systematical analysis of universality in the context of nonabelian gauge theories were made in [10] by investigation of gauge fields with vanishing scalar curvature invariants (V SI gauge fields, for short) and Yang-Mills test fields immune to any highercurvature modification of the Yang-Mills equation.…”

“…In the present contribution, we wish to complete the discussion of [10] by taking into account the spacetime backreaction and draw some general conclusions based on results of the previous works.…”

“…More insight into the nature of these solutions can be gained by employing the characterization of V SI metrics and V SI gauge fields 3 provided in [15,16] and [10], respectively. In particular, g belongs to a subclass of Weyl type III and Ricci type 4 N Kundt metrics and A possesses a null field strength F .…”