The generalised infrared structure of the gluon propagator

Abstract

Gauge theory correlators are potentially more singular in the infrared than those in non-gauge theories. We determine the implications that these singularities have on the spectrum of the theory, proving that the appearance of generalised poles implies the existence of on-shell states with fixed mass, but zero norm. For quantum chromodynamics these poles have direct relevance for the confinement of coloured states. Using lattice data for the Landau gauge gluon propagator we subsequently test for the presence of these poles, establishing that the data is indeed consistent with such a component.

Spectral functions of confined particles

“…[88] it has been shown that the quenched Landau gauge lattice data of [8] can be described (in the Re(q 2 ) > 0 region) in terms of simple and double poles located on the real negative q 2 -axis. These poles (which, incidentally, would not break locality) would in turn correspond to unconventional singular terms (derivatives of the δ-function) present in the spectral representations of unphysical correlators, and which are permitted due to the indefinite metric characterizing covariant gauge theories (see again [88] and references therein). However, the analysis of mock data generated according to these predictions, shows that our method does correctly reconstruct such poles on the real negative q 2 -axis; and, in particular, that it does not mistakenly reconstruct them as complex conjugate pairs, even when noise is added.…”

Lorentzian quantum gravity and the graviton spectral function

“…Therefore, it is quite remarkable that the graviton spectral function and propagator indeed obey the KL spectral representation (2). This noteworthy result should be contrasted with the unclear situation in non-Abelian gauge theories where a similar understanding has not yet been achieved [34,35,[42][43][44][45].…”

Reconstructing the graviton

“…While the photon in QED is believed to have a spectral representation, this is currently a debated subject in QCD, see e.g. [37,76] and references therein. Possible extensions of ( 16) include complex conjugated poles, which are not considered here, as they may signal the loss of unitarity.…”

“…where ' * ' stands for the complete contraction of the projection operators with the vertex. The denominator in (76) takes care of the wave-function renormalisations in (11). The flow ( 76) is evaluated at the momentum symmetric point, see (12), which makes is a function of one single momentum.…”