The QFT description of forces other than gravity assumes some internal symmetry such as the $SU(3)$ color symmetry for strong interactions. Gravity is based on spacetime symmetries. What forbids the theory of gravity to have an internal symmetry, global or local?

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    $\begingroup$ A quantum theory of gravity cannot have global symmetries since we would then have local conserved currents and since there do not exist gauge (diffeomorphism) invariant local operators in gravity. Local gauge symmetries may exist. $\endgroup$ – Prahar May 27 '18 at 14:38
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    $\begingroup$ This reads like answer rather than a comment. $\endgroup$ – my2cts May 27 '18 at 15:49
  • $\begingroup$ Related: physics.stackexchange.com/q/4908/2451 $\endgroup$ – Qmechanic May 27 '18 at 16:08
  • $\begingroup$ A spin $2$ particle can only couple to the energy-momentum tensor, which is neutral under any internal symmetry. Thus, the spin $2$ particle must be as well. $\endgroup$ – AccidentalFourierTransform May 27 '18 at 16:13
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    $\begingroup$ @AccidentalFourierTransform - I think OP is asking whether theories of gravity can have any symmetries whether or not the graviton itself is charged under that symmetry. $\endgroup$ – Prahar May 27 '18 at 16:49

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