4D spin-2 fields from 5D Chern-Simons theory

Abstract

We consider a 5-dimensional Chern-Simons gauge theory for the isometry group of Anti-de-Sitter spacetime, ${\mathrm{AdS}}_{4+1}\simeq \mathrm{SO}(4,2)$, and invoke different dimensional reduction schemes in order to relate it to 4-dimensional spin-2 theories. The AdS gauge algebra is isomorphic to a parametrized 4-dimensional conformal algebra, and the gauge fields corresponding to the generators of non-Abelian translations and special conformal transformations reduce to two vierbein fields in $D=4$. Besides these two vierbeine, our reduction schemes leave only the Lorentz spin connection as an additional dynamical field in the 4-dimensional theories. We identify the corresponding actions as particular generalizations of Einstein-Cartan theory, conformal gravity and ghost-free bimetric gravity in first-order form.

31 pages, no figures, added references

References in corpus (6)

• Interacting Spin-2 Fields
• Einstein Gravity from Conformal Gravity
• The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern--Simons Theory
• Compactification in first order gravity
• Chern-Simons Gravity in Four Dimensions
• D=4 Einstein gravity from higher D CS and BI gravity and an alternative to dimensional reduction