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Register a new userNon-perturbative constraints on the quark and ghost propagators
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Peter Lowdon
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In QCD both the quark and ghost propagators are important for governing the non-perturbative dynamics of the theory. It turns out that the dynamical properties of the quark and ghost fields impose non-perturbative constraints on the analytic structure of these propagators. In this work we explicitly derive these constraints. In doing so we establish that the corresponding spectral densities include components which are multiples of discrete mass terms, and that the propagators are permitted to contain singular contributions involving derivatives of $delta(p)$, both of which are particularly relevant in the context of confinement.
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We study the dominant non-perturbative power corrections to the ghost and gluon propagators in Landau gauge pure Yang-Mills theory using OPE and lattice simulations. The leading order Wilson coefficients are proven to be the same for both propagators. The ratio of the ghost and gluon propagators is thus free from this dominant power correction. Indeed, a purely perturbative fit of this ratio gives smaller value ($simeq 270$MeV) of $Lambda_{ms}$ than the one obtained from the propagators separately($simeq 320$MeV). This argues in favour of significant non-perturbative $sim 1/q^2$ power corrections in the ghost and gluon propagators. We check the self-consistency of the method.
We derive the form of the infrared gluon propagator by proving a mapping in the infrared of the quantum Yang-Mills and $lambdaphi^4$ theories. The equivalence is complete at a classical level. But while at a quantum level, the correspondence is spoiled by quantum fluctuations in the ultraviolet limit, we prove that it holds in the infrared where the coupling constant happens to be very large. The infrared propagator is then obtained from the quantum field theory of the scalar field producing a full spectrum. The results are in fully agreement with recent lattice computations. We get a finite propagator at zero momentum, the ghost propagator going to infinity as $1/p^{2+2kappa}$ with $kappa=0$.
We derive general properties of the scale-dependent effective spectral dimensions of non-perturbative gauge boson propagators as they appear as solutions from different methods in Yang-Mills theories. In the ultraviolet and for short time scales the anomalous dimensions of the propagators lead to a slight decrease of the spectral dimension as compared to the one of a free propagator. Lowering the momentum scale, the spectral dimension decreases further. The class of propagators which display a maximum at Euclidean momenta, and thus violate positivity, always approaches a spectral dimension of one for large times. We also show that the longest time intervals are not related to the deep infrared but to the momentum scale defined by the position of the maximum.
Starting from the lattice Landau gauge gluon and ghost propagator data we use a sequence of Pade approximants, identify the poles and zeros for each approximant and map them into the analytic structure of the propagators. For the Landau gauge gluon propagator the Pade analysis identifies a pair of complex conjugate poles and a branch cut along the negative real axis of the Euclidean $p^2$ momenta. For the Landau gauge ghost propagator the Pade analysis shows a single pole at $p^2 = 0$ and a branch cut also along the negative real axis of the Euclidean $p^2$ momenta. The method gives precise estimates for the gluon complex poles, that agree well with other estimates found in the literature. For the branch cut the Pade analysis gives, at least, a rough estimate of the corresponding branch point.
In recent times, a considerable effort has been dedicated to identify certain conditions -- the so-called swampland conjectures -- with an eye on identifying effective theories which have no consistent UV-completions in string theory. In this paper, we examine the anti-de Sitter vacua corresponding to solutions which arise from purely non-perturbative contributions to the superpotential and show that these solutions satisfy the (axionic) weak gravity conjecture and the AdS-moduli scale separation conjecture. We also sketch out their advantages over other constructions.
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