First, let me state the form of Lagrangian for YM and GR \begin{align} L_{YM} = \alpha \textrm{tr}(F^2), \qquad L_{GR} = \beta R \end{align} I heard, YM is a gauge theory but GR isn't a really gauge theory. Due to the fact of its Cartan-Killing form of YM is positive, but GR is negative. Is it valid approach?
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