For semisimple Lie algebra targets
For discrete group targets
For discrete 2-group targets
For Lie 2-algebra targets
For targets extending the super Poincare Lie algebra
for higher abelian targets
for symplectic Lie n-algebroid targets
In the first order formulation of gravity the Einstein-Hilbert action in dimension 3 happens to be equivalent to the action functional of Chern-Simons theory for connections with values in the Poincare Lie algebra (spin connection and vielbein, for a suitable quadratic invariant polynomial. Similarly for 3-dimensional supergravity. See 3d quantum gravity.
Generally, for every higher degree (-ary) invariant polynomial on the Poincaré Lie algebra there is the corresponding higher dimensional Chern-Simons theory in dimension . These Chern-Simons type action functionals all include the Einstein-Hilbert action linear in the curvature as a summand, but generally contain higher degree curvature invariants. A theory of Chern-Simons gravity is a field theory governed by such an action functional.
While there is no experimental evidence for such higher curvature terms in the theory of gravity, there exist parameter regions in which their predicted effects are smaller than could have been observed. Moreover, there are varous suggestions that under Inönü-Wigner contraction? of the AdS Lie algebra? to the Poincare Lie algebra, and -Chern-Simons gravity theory could be close to an ordinary einstein-Hilbert theory.
In view of this, the fact that Chern-Simons action functionals are singled out by their nice formal properties has led to various speculations that possibly the fundamental theory of gravity is secretly a theory of Chern-Simons gravity after all (see the References). Whether that is true or not, certainly in the general mathematical context of infinity-Chern-Simons theory the study of Chern-Simons gravity is natural and interesting.
Warning In parts of the literature the term Chern-Simons grvaity is used for the modificaton of the Einstein-Hilbert action in 4-dimensions obtained by adding to the standard action the Pontryagin class term for the Riemann curvature. This is however not a Chern-Simons action functional in the strict sense of the term.
The original articles that considered 3-dimensional gravity as a Chern-Simons theory are
A. Achúcarro and P. Townsend, A Chern-Simons Action for Three-Dimensional anti-De Sitter Supergravity Theories , Phys. Lett. B180 (1986) 89.
Further developments are in
A review of some aspects is in
Boundaries in 3d Chern-Simons gravity and relation to the WZW model are discussed for instance in
See also 3d quantum gravity.
An introduction and survey is in
More along these lines is in
Original articles include
Máximo Bañados, Higher dimensional Chern-Simons theories and black holes (pdf)
Máximo Bañados, Ricardo Troncoso, Jorge Zanelli, Higher dimensional Chern-Simons supergravity Phys. Rev. D 54, 2605–2611 (1996)
Jorge Zanelli, Chern–Simons forms and transgression actions or the universe as a subsystem Journal of Physics: Conference Series Volume 68 Volume 68
Hitoshi Nishino and Subhash Rajpoot, Supersymmetric Lorentz Chern-Simons terms coupled to supergravity Phys. Rev. D 81, 085029 (2010)
A speculation that 11-dimensional supergravity is naturally to be understood as a contraction limit of a Chern-Simons supergravity theory was put forward in
with further developments in
Other approaches to 11d Chern-Simons supergravity include
There is an 6-ary invariant polynomial of degree on the M-theory super Lie algebra. Using its Chern-Simons element as the Lagrangian for an infinity-Chern-Simons theory yields an 11-dimensional supersymmetric field theory different from but maybe related to 11-dimensional supergravity. This is discussed in
J. Gegenberg , G. Kunstatter, Boundary Dynamics of Higher Dimensional Chern-Simons Gravity (arXiv:hep-th/0010020)
J. Gegenberg , G. Kunstatter, Boundary Dynamics of Higher Dimensional AdS Spacetime (arXiv:http://arxiv.org/abs/hep-th/9905228)