# Why does gravity forbid local observables?

I heard in a conference that gravity forbids to construct local gauge invariants like $\mathrm{Tr}\left\{−\frac{1}{4} F_{μν}^{a}F_{a}^{μν}\right\}$ and only allows non-local gauge invariant quantities like Wilson Loops: $\mathrm{Tr}\mathcal{P}\exp\left[\oint_{\gamma} A^{a}dx_{a}\right]$. Could someone explain me where does it come from?

• I am sorry but it still isn't clear for me, if I build a theory containing general coordinate invariance and U(1) local gauge symmetry, so a "world" containing gravity and electromagnetism, and I minimally couple the gauge boson to gravity, ie his kinetic term is $-\frac14 F^{\mu\nu}F_{\mu\nu}$ with $F_{\mu\nu} = D_{\mu}A_{\nu} - D_{\nu}A_{\mu}$ where $D$ is the covariant derivative associated with coordinate-diffeomorphisms, so this term is a scalar regarding both gauge and coordinate transformations; thus a good candidate for a local observable. – toot Sep 11 '11 at 13:49