What is the Spin Connection Equation for Gauging the Poincare Group?

[shereen1]

Dear All
in the idea of gauging Poincare group i am trying to find the equation of motion of the spin connection w_mu^ab using Euler Lagrange equation. but it seems that i am not getting the same terms
can i have a help. I know that this equation is equivalent to the torsionless condition, but i want to get it in the other way starting from the action and applying euler lagrange.
thank you

 

[haushofer]

http://www.itp.uni-hannover.de/saalburg/Lectures/samtleben.pdf

Eqn. (25) and Appendix A should help.

 

[mhob]

The appendix of the paper `Actions for Gravity ...' by Peldan may can help you.