Dimensionally Reduced Gravitational Chern-Simons Term and its Kink

TL;DR

Dimensional reduction of the 3D gravitational Chern-Simons term yields a 2D topological gravity theory with a symmetry-breaking sector and a kink solution. The KK reduction reveals an axion-Chern-Pontryagin structure, with EOM supporting both symmetry-preserving and symmetry-breaking vacua; the kink interpolates between these vacua and creates a geometry that is asymptotically AdS while exhibiting localized curvature. The work draws a deep parallel between general relativistic kinks and flat-space kinks through a shared potential, suggesting dilaton-like connections and inviting extensions to higher-dimensional reductions. Overall, the paper demonstrates how topological gravitational terms can generate nontrivial solitonic structures and rich geometric behavior in lower dimensions, with potential implications for other dimensional reductions and field-theoretic generalizations.

Abstract

When the gravitational Chern-Simons term is reduced from 3 to 2 dimensions, the lower dimensional theory supports a symmetry breaking solution and an associated kink. Kinks in general relativity bear a close relation to flat space kinks, governed by identical potentials.