Asymptotic safety on the lattice: The nonlinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si84.gif" display="inline" overflow="scroll"><mml:mstyle mathvariant="normal"><mml:mi>O</mml:mi></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> sigma model

Wellegehausen, Björn; Körner, Daniel; Wipf, Andreas

doi:10.1016/j.aop.2014.06.024

Cited by 11 publications

(5 citation statements)

References 45 publications

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“…Using (6), (7), and Tab. 2, we find ∆a ≡ a UV − a IR > 0 (14) on any of the UV-IR connecting trajectories in the parameter ranges (10), (11) shown in Fig. 1.…”

Section: Gymentioning

confidence: 74%

“…Asymptotic safety explains how theories can be fundamental, predictive, and interacting at highest energies [6]. Initially put forward as a scenario to quantize gravity [7][8][9][10], asymptotic safety also arises in many other theories [11][12][13][14]. In particle physics, asymptotic safety offers intriguing new directions to ultraviolet (UV) complete the Standard Model beyond the confines of asymptotic freedom [15][16][17].…”

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confidence: 99%

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Asymptotic Safety Guaranteed in Supersymmetry

Bond¹

2017

Phys. Rev. Lett.

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We explain how asymptotic safety arises in four-dimensional supersymmetric gauge theories. We provide asymptotically safe supersymmetric gauge theories together with their superconformal fixed points, R charges, phase diagrams, and UV-IR connecting trajectories. Strict perturbative control is achieved in a Veneziano limit. Consistency with unitarity and the a theorem is established. We find that supersymmetry enhances the predictivity of asymptotically safe theories. DOI: 10.1103/PhysRevLett.119.211601 Introduction.-The discovery of asymptotic freedom for non-Abelian gauge theories in 1973 has initiated a new era in particle physics [1,2]. Asymptotic freedom explains why certain types of quantum field theories such as the strong and weak sector of the standard model can be truly fundamental and predictive up to the highest energies. It implies that interactions are switched off asymptotically and theories become free. Asymptotic freedom constitutes a cornerstone in the standard model of particle physics and continues to play an important role in the search for models beyond.The discovery of exact asymptotic safety for nonAbelian gauge theories with matter [3-5] has raised substantial interest. Asymptotic safety explains how theories can be fundamental, predictive, and interacting at highest energies [6]. Initially put forward as a scenario to quantize gravity [7][8][9][10], asymptotic safety also arises in many other theories [11][12][13][14]. In particle physics, asymptotic safety offers intriguing new directions to ultraviolet (UV) complete the standard model beyond the confines of asymptotic freedom [15][16][17].In this Letter, we investigate whether asymptotic safety can be achieved in supersymmetric gauge theories. In the language of the renormalization group (RG), asymptotic safety corresponds to an interacting UV fixed point for the running couplings [6]. Supersymmetry modifies fixed points and the evolution of couplings, because it links bosonic with fermionic degrees of freedom [4,18,19]. Additional constraints arise as bounds on the superconformal R charges [20] from both unitarity [21] and the a theorem [22][23][24][25]. Hence, our task consists of finding supersymmetric gauge theories without asymptotic freedom, but with viable interacting UV fixed points, and in accord with all constraints.One arena in which we may hope to find reliable answers is that of perturbation theory. For sufficiently small couplings [26], the loop expansion and weakly interacting fixed points are trustworthy [4]. In this spirit, we obtain fixed points, phase diagrams, superconformal R charges, and UV-IR connecting trajectories for supersymmetric gauge theories in a controlled setting. Previously, this

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“…Using (6), (7), and Tab. 2, we find ∆a ≡ a UV − a IR > 0 (14) on any of the UV-IR connecting trajectories in the parameter ranges (10), (11) shown in Fig. 1.…”

Section: Gymentioning

confidence: 74%

mentioning

confidence: 99%

Asymptotic Safety Guaranteed in Supersymmetry

Bond¹

2017

Phys. Rev. Lett.

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“…We hope that our findings serve as an inspiration for searches for non-Gaußian fixed points in QED using other nonperturbative methods: Within functional methods, vertex expansions offer a powerful expansion scheme; in fact, vertex structures overlapping with the Pauli term are found to play an important role in the strong coupling region of QCD [71]. New lattice searches would need to go beyond the standard bare QED lattice action and also require an explicit parametrization of the Pauli term and a corresponding independent coupling; for an example of asymptotic safety discovered on the lattice in a scalar model, see [72]. Studying the existence of these fixed points would also be an interesting target for the conformal bootstrap along the lines of [73].…”

Section: Discussionmentioning

confidence: 99%

Asymptotically safe QED

Gies

Ziebell

2020

Eur. Phys. J. C

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High-energy completeness of quantum electrodynamics (QED) can be induced by an interacting ultraviolet fixed point of the renormalization flow. We provide evidence for the existence of two of such fixed points in the subspace spanned by the gauge coupling, the electron mass and the Pauli spin-field coupling. Renormalization group trajectories emanating from these fixed points correspond to asymptotically safe theories that are free from the Landau pole problem. We analyze the resulting universality classes defined by the fixed points, determine the corresponding critical exponents, study the resulting phase diagram, and quantify the stability of our results with respect to a systematic expansion scheme. We also compute high-energy complete flows towards the long-range physics. We observe the existence of a renormalization group trajectory that interconnects one of the interacting fixed points with the physical low-energy behavior of QED as measured in experiment. Within pure QED, we estimate the crossover from perturbative QED to the asymptotically safe fixed point regime to occur somewhat above the Planck scale but far below the scale of the Landau pole.

show abstract

“…We hope that our findings serve as an inspiration for searches for non-Gaußian fixed points in QED using other nonperturbative methods: Within functional methods, vertex expansions offer a powerful expansion scheme; in fact, vertex structures overlapping with the Pauli term are found to play an important role in the strong coupling region of QCD [67]. New lattice searches would need to go beyond the standard bare QED lattice action and also require an explicit parametrization of the Pauli term and a corresponding independent coupling; for an example of asymptotic safety discovered on the lattice in a scalar model, see [68]. Studying the existence of these fixed points would also be an interesting target for the conformal bootstrap along the lines of [69].…”

Section: Discussionmentioning

confidence: 99%

Asymptotically Safe QED

Gies,

Ziebell

2020

Preprint

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Asymptotic safety on the lattice: The nonlinear O(N) sigma model

Cited by 11 publications

References 45 publications

Asymptotic Safety Guaranteed in Supersymmetry

Asymptotic Safety Guaranteed in Supersymmetry

Asymptotically safe QED

Asymptotically Safe QED

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