Reconstructing propagators of confined particles in the presence of complex singularities

We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The reconstruction is applied to both the dynamical fluctuation graviton and the background graviton propagator. We prove that the spectral function of the latter necessarily has negative parts similar to, and for the same reasons, as the gluon spectral function. In turn, the spectral function of the dynamical graviton is positive. We argue that the latter enters cross sections and other observables in asymptotically safe quantum gravity. Hence, its positivity may hint at the unitarity of asymptotically safe quantum gravity.

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“…However, for recent discussions of such an extension including the question of unitarity see e.g. [77][78][79][80].…”

Section: Properties Of the Graviton Spectral Functionmentioning

confidence: 99%

Reconstructing the graviton

et al. 2022

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“…In what follows, we mainly discuss the following two questions corresponding to the arrows (α) and (β) in Fig. 2 We will answer these questions affirmatively [9,10].…”

Section: Main Questionsmentioning

confidence: 83%

“…In this light, it can be said that complex singularities correspond to confined states. We can also argue that the existence of complex singularities in a propagator of the gluon-ghost composite operator is a necessary condition for this scenario 4 [10].…”

Section: Realization In Quantum Theorymentioning

confidence: 98%

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Rigorous reconstruction of gluon propagator in the presence of complex singularities

Hayashi¹,

Kondo²

2021

Preprint

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It has been suggested that the Landau-gauge gluon propagator has complex singularities, which invalidates the Källén-Lehmann spectral representation. Since such singularities are beyond the standard formalism of quantum field theory, the reconstruction of Minkowski propagators from Euclidean propagators has to be carefully examined for their interpretation. In this talk, we present rigorous results on this reconstruction in the presence of complex singularities. As a result, the analytically continued Wightman function is holomorphic in the usual tube, and the Lorentz symmetry and locality are kept valid. On the other hand, the Wightman function on the Minkowski spacetime is a non-tempered distribution and violates the positivity condition. Finally, we discuss an interpretation and implications of complex singularities in quantum theories, arguing that complex singularities correspond to zero-norm confined states.

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“…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].…”

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confidence: 81%

Lorentzian quantum gravity and the graviton spectral function

Fehre¹,

Pawlowski²,

Reichert³

2021

Preprint

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We present the first direct and non-perturbative computation of the graviton spectral function in quantum gravity. This is achieved with the help of a novel Lorentzian renormalisation group approach, combined with a spectral representation of correlation functions. We find a positive graviton spectral function, showing a massless one-graviton peak and a multi-graviton continuum with an asymptotically safe scaling for large spectral values. We also study the impact of a cosmological constant. Further steps to investigate scattering processes and unitarity in asymptotically safe quantum gravity are indicated.

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Reconstructing propagators of confined particles in the presence of complex singularities

Cited by 18 publications

References 67 publications

Reconstructing the graviton

Reconstructing the graviton

Rigorous reconstruction of gluon propagator in the presence of complex singularities

Lorentzian quantum gravity and the graviton spectral function

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