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I don't think it is clear to me what exactly is the physical meaning of the energy-momentum tensor being traceless.

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    $\begingroup$ Related: physics.stackexchange.com/q/162297/2451 $\endgroup$ – Qmechanic Jan 26 '17 at 12:13
  • $\begingroup$ It means the theory is invariant under conformal transformation. For example, Pure bosonic string theory has 2D conformal invariance. Therefore it is scale invariant. $\endgroup$ – AMS Jan 26 '17 at 12:29
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    $\begingroup$ What sort of "physical meaning" are you looking for? Is "the theory is dilatation invariant" a "physical meaning"? $\endgroup$ – ACuriousMind Jan 26 '17 at 14:05
  • $\begingroup$ Ok! That's clear. @ACuriousMind i was also wondering if it had something to do with the field being massless or massive $\endgroup$ – user129511 Jan 26 '17 at 14:56
  • $\begingroup$ @user129511 If the field was massive, the theory wouldn't have conformal invariance, as the mass introduces a scale $\endgroup$ – coconut Jan 26 '17 at 15:40

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