General relativity from a gauged Wess-Zumino-Witten term

Abstract

In this paper two things are done. First it is shown how a four dimensional gauged Wess-Zumino-Witten term arises from the five dimensional Einstein-Hilbert plus Gauss-Bonnet lagrangian with a special choice of the coefficients. Second, the way in which the equations of motion of fourdimensional General Relativity arise is exhibited.

Universe as a topological defect

“…While in QCD the gWZW term describes the interactions of the infrared sector of the theory, here it might correspond to an ultraviolet extension of GR. The action (16) was proposed as a gravitational model in [18] where, in order to obtain Einstein's field equations, a field was fixed in the action. That is a rather unsatisfactory situation since this is a condition imposed on a theory by an a posteriori expected result.…”

“…r is the bilinear invariant of the Lie group, and A µ is the Lie algebra valued connection-, never arises in our construction [18]. The resulting action resembles in many ways its three-dimensional, quantum mechanically finite sibling: in both cases e and ω are part of a single SO(m, n) connection A; both theories admit a vacuum configuration e = ω = 0, in which the space-time causal structure completely disappears; both have a quantized dimensionless "coupling" constant in front of the action.…”

Some considerations on the Mac Dowell-Mansouri action

“…Now, the main problem to obtain Einstein gravity from the gWZW term is that equations quadratic in the curvature arise when the field equations associated to the non-linear sigma model are taken in account [9,10]. Thus, in configurations of constant φ, the system become overconstrained and, for instance, the unique spherically symmetric solution is flat space [24].…”

“…As is discussed in [9,10] CS theories and gWZW forms are intriscally related, thus, they define our starting point to construct a gauge theory of gravity in even dimensions.…”

“…On the other hand it has been pointed out that due to the natural connection between Chern-Simons forms and gauged Wess-Zumino-Witten (gWZW) terms [9,10] they should correspond to even dimensional gauge theories of gravity. Since the above approach and the Chamseddine-Mac Dowell-Mansouri-Stelle-West (CMMSW) one contains similar ingredients, namely some 0-form fields and a gauge connection, it could be expected that they should share some similarity.…”