Analytic coupling structure of large 
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 (super) QED and QCD

Dondi, Nicola Andrea; Dunne, Gerald V.; Reichert, Manuel; Sannino, Francesco

doi:10.1103/physrevd.100.015013

Cited by 17 publications

(19 citation statements)

References 43 publications

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“…Nevertheless specialising [11] to the case in which asymptotic freedom is lost (N f ≥ 3N c ) for super QCD with(out) a meson [11,53] one can show that these theories are unsafe for any number of matter fields. This is in agreement with the 1/N f studies of the supersymmetric beta functions [53,58] as explained in [35]. The unsafety of super QCD with(out) a meson should be contrasted with QCD at large number of flavors for which, as we argued above, safety is possible [31] and QCD with a meson for which safety is a fact [12].…”

Section: Conformal Window 20: Review Of the Analytic Resultssupporting

confidence: 89%

“…Unfortunately, the positivity of the coefficients is insufficient to prove the stability of the series and determine its radius of convergence. The first complete study of the analytic properties of the leading nontrivial large-N f expansion appeared recently in [35]. Here it was demonstrated that an analysis of the expansion coefficients to roughly 30 orders is required to establish the radius of convergence accurately, and to characterize the (logarithmic) nature of the first beta function singularity.…”

Section: Conformal Window 20: Review Of the Analytic Resultsmentioning

confidence: 99%

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Safety versus triviality on the lattice

et al. 2020

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We present the first numerical study of the ultraviolet dynamics of non-asymptotically free gaugefermion theories at large number of matter fields. As testbed theories we consider non-abelian SU(2) gauge theories with 24 and 48 Dirac fermions on the lattice. For these number of flavors asymptotic freedom is lost and the theories are governed by a gaussian fixed point at low energies. In the ultraviolet they can develop a physical cutoff and therefore be trivial, or achieve an interacting safe fixed point and therefore be fundamental at all energy scales. We demonstrate that the gradient flow method can be successfully implemented and applied to determine the renormalized running coupling when asymptotic freedom is lost. Additionally, we prove that our analysis is connected to the gaussian fixed point as our results nicely match with the perturbative beta function. Intriguingly, we observe that it is hard to achieve large values of the renormalized coupling on the lattice. This might be an early sign of the existence of a physical cutoff and imply that a larger number of flavors is needed to achieve the safe fixed point. A more conservative interpretation of the results is that the current lattice action is unable to explore the deep ultraviolet region where safety might emerge. Our work constitutes an essential step towards determining the ultraviolet fate of non asymptotically free gauge theories.

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Section: Conformal Window 20: Review Of the Analytic Resultssupporting

confidence: 89%

Section: Conformal Window 20: Review Of the Analytic Resultsmentioning

confidence: 99%

Safety versus triviality on the lattice

et al. 2020

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“…In the last section, we have explained that fixed points can also be interacting, which generalises asymptotic freedom to asymptotic safety. Asymptotic safety can show up in a perturbative way as in the Litim-Sannino model [66,67] or in a non-perturbative way, as in quantum gravity [69], gauge theories at large N f [70][71][72][73][74][75] or other matter models [76]. It is very challenging to prove the existence of a non-perturbative fixed point and thus we just state that these theories might be asymptotically safe.…”

Section: Choice Of the Bare Actionmentioning

confidence: 99%

Lecture notes: Functional Renormalisation Group and Asymptotically Safe Quantum Gravity

Reichert¹

2020

Proceedings of XV Modave Summer School in Mathematical Physics — PoS(Modave2019)

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These lecture notes give an introduction to the functional renormalisation group and asymptotically safe quantum gravity. We cover the basics of generating functionals in quantum field theories and derive the Wetterich equation. The anharmonic oscillator is presented as a simple example and compared to perturbation theory with resummation methods. A special focus is set on the implementation of symmetries in the functional renormalisation group. The second half of these notes is dedicated to quantum gravity, explaining the failure of perturbative gravity and how these issues are addressed in the non-perturbative approach. After detailing the implementation of the diffeomorphism symmetry, we present a simple computation in the Einstein-Hilbert truncation and give a short outlook on the state-of-the-art in the field. These notes are based on lectures given at the XV Modave Summer School in Mathematical Physics.

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“…This was first studied in Abelian gauge theory in [1] and in the non-Abelian case in [2]. Recently, there has been a revived interest in asymptotically safe four-dimensional quantum field theories, with particular emphasis on pure fermionic gauge theories, chiral gauge theories, gauge-Yukawa theories involving both scalars and fermions and theories with or without supersymmetry [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Safe glueballs and baryons

Ryttov

Tuominen

2019

J. High Energ. Phys.

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We consider a non-Abelian gauge theory with N f fermions and discuss the possible existence of a non-trivial UV fixed point at large N f . Specifically, we study the anomalous dimension of the (rescaled) glueball operator Tr F 2 to first order in 1/N f by relating it to the derivative of the beta function at the fixed point. At the fixed point the anomalous dimension violates its unitarity bound and so the (rescaled) glueball operator is either decoupled or the fixed point does not exist. We also study the anomalous dimensions of the two spin-1/2 baryon operators to first order in 1/N f for an SU(3) gauge theory with fundamental fermions and find them to be relatively small and well within their associated unitarity bounds.

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Analytic coupling structure of large Nf (super) QED and QCD

Cited by 17 publications

References 43 publications

Safety versus triviality on the lattice

Safety versus triviality on the lattice

Lecture notes: Functional Renormalisation Group and Asymptotically Safe Quantum Gravity

Safe glueballs and baryons

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