Landau-Khalatnikov-Fradkin transformation and the mystery of even 
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-values in Euclidean massless correlators

Kotikov, A. V.; Teber, S.

doi:10.1103/physrevd.100.105017

Cited by 31 publications

(53 citation statements)

References 58 publications

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“…We further could verify that upon adopting theĜ scheme, which involves the redefinition of odd zeta values in terms of an epsilon expansion containing even zeta values -in our case justζ 3 = ζ 3 − 3 4 ζ 4 -all ζ 4 terms vanished in our results for the Z-factors. So all ζ 4 terms in the Z-factors can be fully reconstructed from the existing ζ 3 ones following the "no-π theorem" [81,82].…”

Section: Appendix A: Tool Chainmentioning

confidence: 99%

Abelian Higgs model at four loops, fixed-point collision, and deconfined criticality

et al. 2019

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The abelian Higgs model is the textbook example for the superconducting transition and the Anderson-Higgs mechanism, and has become pivotal in the description of deconfined quantum criticality. We study the abelian Higgs model with n complex scalar fields at unprecedented four-loop order in the 4 − expansion and find that the annihilation of the critical and bicritical points occurs at a critical number of nc ≈ 182.95 1 − 1.752 + 0.798 2 + 0.362 3 + O 4 . Consequently, below nc, the transition turns from second to first order. Resummation of the series to extract the result in three-dimensions provides strong evidence for a critical nc(d = 3) which is significantly below the leading-order value, but the estimates for nc are widely spread. Conjecturing the topology of the renormalization group flow between two and four dimensions, we obtain a smooth interpolation function for nc(d) and find nc(3) ≈ 12.2 ± 3.9 as our best estimate in three dimensions. Finally, we discuss Miransky scaling occurring below nc and comment on implications for weakly first-order behavior of deconfined quantum transitions. We predict an emergent hierarchy of length scales between deconfined quantum transitions corresponding to different n.

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Section: Appendix A: Tool Chainmentioning

confidence: 99%

Abelian Higgs model at four loops, fixed-point collision, and deconfined criticality

et al. 2019

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“…Yet another convenient choice of scale is the minimal Vladimirov-scale [11] which is defined via the relation…”

Section: Mv-scalementioning

confidence: 99%

“…Following [15], a slight modification of this scale that was referred to as the g-scale in [11] subtracts an additional factor 1/(1 − 2ε) from the one-loop result, i.e.,…”

Section: Appendix A: Other Choices Of Scalementioning

confidence: 99%

Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

2020

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We study the gauge-covariance of the massless fermion propagator in reduced Quantum Electrodynamics (QED). Starting from its value in some gauge, we evaluate an all order expression for it in another gauge by means of the Landau-Khalatnikov-Fradkin (LKF) transformation. We find that the weak coupling expansions thus derived are in perfect agreement with the exact calculations. We also prove that the fermion anomalous dimension of reduced QED is gauge invariant to all orders of perturbation theory except for the first one.

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“…Furthermore, the cosmic Galois group would imply that together with ζ (2), also all products with odd zeta values (like ζ (2)ζ ( 3)) would be excluded as periods of graphs. For a discussion of these ideas we refer to [19,20], and physical interpretations of the absence of ζ (2) are given in [2,33].…”

Section: Families Of Graphs With Polylogarithmic Periodsmentioning

confidence: 99%

Some Open Problems on Feynman Periods

Panzer¹

2020

Springer Proceedings in Mathematics &Amp; Statistics

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Feynman integrals of quantum field theories that contain non-scalar particles go beyond the well-studied leading period associated to primitive Feynman graphs. It is therefore necessary to study the space of periods spanned by all convergent Feynman integrals for a given graph. Even when the leading period is known, this total space of periods is not understood and carries non-trivial structures. After reviewing the leading period, we consider all convergent integrals of a graph and related open questions.

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Landau-Khalatnikov-Fradkin transformation and the mystery of even ζ -values in Euclidean massless correlators

Cited by 31 publications

References 58 publications

Abelian Higgs model at four loops, fixed-point collision, and deconfined criticality

Abelian Higgs model at four loops, fixed-point collision, and deconfined criticality

Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

Some Open Problems on Feynman Periods

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