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In chapter 4 of Bailin & Love,

I just wanted to ask, that the Poincaré algebra also contains the generator of translations (of course), and if we take that to be a local symmetry, do we just get GR plain and simple? Or something else?

*Supersymmetric gauge field theory and string theory*, the authors state that supersymmetry is considered a global symmetry, and we can separately consider it to be a local symmetry. Further, since the supersymmetry algebra contains [itex]P^\mu[/itex], the generator of translations, we would also get local translation invariance, and this is a theory of gravitation, as per GR, and is called supergravity.I just wanted to ask, that the Poincaré algebra also contains the generator of translations (of course), and if we take that to be a local symmetry, do we just get GR plain and simple? Or something else?

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