# Supergravity action as a total integral, over 4 spacetime and 4 Grassmann coordinates

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Wess and Bagger, in their Supersymmetry and Supergravity, give the action for a global SUSY, ${\cal N}=1$, $D=4$, Yang-Mills gauge model as an integral over the 4 spacetime coordinates and 4 Grassmann coordinates, and also give an alternative formulation over 4 spacetime and just 2 Grassmann coordinates. I am okay with this. When they locally gauge the global SUSY transform to get supergravity they only give the formulation over 4 spacetime plus 2 Grassmann coordinates. What is the supergravity action in the 4+4-integral form? The rules they give, for going from SUSY to SUGra seem ambiguous, especially with regards to the chiral density. Any links to the explicit construction would be appreciated.

This post imported from StackExchange Physics at 2018-01-20 17:49 (UTC), posted by SE-user Michael C Price

edited Jan 20, 2018

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