General relativity and supergravity in all dimensions meet each other at a common assumption: Any configuration space can be coordinatized by gauge fields A a i {\displaystyle A_{a}^{i}} , where the index i {\displaystyle i} is a Lie algebra index and a {\displaystyle a} is a spatial manifold index. Using these assumptions one can construct an effective field theory in low energies for both.
General relativity and supergravity in all dimensions meet each other at a common assumption: Any configuration space can be coordinatized by gauge fields A a i {\displaystyle A_{a}^{i}} , where the index i {\displaystyle i} is a Lie algebra index and a {\displaystyle a} is a spatial manifold index. Using these assumptions one can construct an effective field theory in low energies for both.
Source: Wikipedia "Plebanski action" · CC BY-SA 4.0
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