Asymptotic safety of scalar field theories

Trott, M.

doi:10.1103/physrevd.98.125006

Cited by 33 publications

(52 citation statements)

References 157 publications

(529 reference statements)

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“…The situation becomes even more complex when adding fermions. There are some investigations using functional methods of such theories, but focusing on a field content which makes the effective interaction strength weak [224,225]. There are, of course, many results using perturbation theory [84,163,179].…”

Section: The Phase Diagram From the Latticementioning

confidence: 99%

“…In fact, arguments using the functional renormalization group have been given that there should exist an interacting continuum limit at weak Higgs self-coupling [203,206,385], which is not excluded by studies of these regions on the lattice [162,275]. Furthermore, fermions can potentially influence the qualitative behavior already at the perturbative level [143,224,225,386], but also non-perturbatively [387]. This does not even mention the influence of more extreme settings, like extended Higgs potentials 86 [302] or the influence of quantum gravity [347,348,389,390].…”

Section: The Triviality Problemmentioning

confidence: 99%

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Brout–Englert–Higgs physics: From foundations to phenomenology

Maas

2019

Progress in Particle and Nuclear Physics

107

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Brout-Englert Higgs physics is one of the most central and successful parts of the standard model. It is also part of a multitude of beyond-the-standard-model scenarios.The aim of this review is to describe the field-theoretical foundations of Brout-Englert-Higgs physics, and to show how the usual phenomenology arises from it. This requires to give a precise and gauge-invariant meaning to the underlying physics. This is complicated by the fact that concepts like the Higgs vacuum expectation value or the separation between confinement and the Brout-Englert-Higgs effect loose their meaning beyond perturbation theory. This is addressed by carefully constructing the corresponding theory space and the quantum phase diagram of theories with elementary Higgs fields and gauge interactions.The physical spectrum needs then to be also given in terms of gauge-invariant, i. e. composite, states. Using gauge-invariant perturbation theory, as developed by Fröhlich, Morchio, and Strocchi, it is possible to rederive conventional perturbation theory in this framework. This derivation explicitly shows why the description of the standard model in terms of the unphysical, gaugedependent, elementary states of the Higgs and W -bosons and Z-boson, but also of the elementary fermions, is adequate and successful.These are unavoidable consequences of the field theory underlying the standard model, from which the usual picture emerges. The validity of this emergence can only be tested non-perturbatively. Such tests, in particular using lattice gauge theory, will be reviewed as well. They fully confirm the underlying mechanisms.In this course it will be seen that the structure of the standard model is very special, and qualitative changes occur beyond it. The extension beyond the standard model will therefore also be reviewed. Particular attention will be given to structural differences arising for phenomenology. Again, non-perturbative tests of these results will be reviewed.Finally, to make this review self-contained a brief discussion of issues like the triviality and hierarchy problem, and how they fit into a fundamental field-theoretical formulation, is included. If there is no gauge-invariant way of defining the vacuum expectation value of the Higgs, the whole standard procedure [14] of doing BEH physics seems to collapse on itself at first. This seems to question the whole basis of the current theoretical description of experiments, despite its huge success [10]. But it does not. Rather, it can be shown that a treatment taking the gauge-dependence into account will lead to, essentially, the same results for the standard model.How this works out is exactly the core of this review: The construction of a fully gauge-invariant description of this physics, and how the standard phenomenology follows from it. This starts in section 3. There, a gauge-invariant description of the theory (3) will be set up. This is the first step of developing a comprehensive, field-theoretical consistent view on BEH physics. This view is continued by establis...

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Section: The Phase Diagram From the Latticementioning

confidence: 99%

Section: The Triviality Problemmentioning

confidence: 99%

Brout–Englert–Higgs physics: From foundations to phenomenology

Maas

2019

Progress in Particle and Nuclear Physics

107

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“…These trajectories fully realize quantum scale invariance. In the scalar theory in four dimensions that we have considered here as an example, the only such fixed point is the free theory, but there exist nontrivial fixed points in less than four dimensions and there are other examples of four-dimensional field theories with nontrivial fixed points [31].…”

mentioning

confidence: 99%

Trace anomaly and infrared cutoffs

Morris

Percacci

2019

Phys. Rev. D

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The Effective Average Action is a form of effective action which depends on a cutoff scale suppressing the contribution of low momentum modes in the functional integral. It reduces to the ordinary effective action when the cutoff scale goes to zero. We derive the modifications of the scale Ward identity due to this cutoff and show how the resulting identity then intimately relates the trace anomaly to the Wilsonian realisation of the renormalization group.

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“…For gravity, several calculations based on truncated Exact Renormalization Group Equations (ERGE) support the conjecture that there is an interacting fixed point in the ultraviolet [22][23][24][25][26][27][28][29][30]. Support for the conjecture also comes from calculations for gravity with matter or a cosmological constant [31][32][33][34][35][36][37]. Then there is an asymptotically safe quantum theory of gravity -however, the truncation implies that the effective low energy theory is scale-dependent.…”

Section: Introductionmentioning

confidence: 98%

Cosmology of Bianchi type-I metric using renormalization group approach for quantum gravity

Mandal

Gangopadhyay

Lahiri

2020

Class. Quantum Grav.

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We study the anisotropic Bianchi type-I cosmological model at late times, taking into account quantum gravitational corrections in the formalism of the exact renormalization group flow of the effective average action for gravity. The cosmological evolution equations are derived by including the scale dependence of Newton's constant G and cosmological constant Λ. We have considered the solutions of the flow equations for G and Λ at next to leading order in the infrared cutoff scale.Using these scale dependent G and Λ in Einstein equations for the Bianchi-I model, we obtain the scale factors in different directions. It is shown that the scale factors eventually evolve into FLRW universe for known matter like radiation. However, for dust and stiff matter we find that the universe need not evolve to the FLRW cosmology in general, but can also show Kasner type behaviour.

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Asymptotic safety of scalar field theories

Cited by 33 publications

References 157 publications

Brout–Englert–Higgs physics: From foundations to phenomenology

Brout–Englert–Higgs physics: From foundations to phenomenology

Trace anomaly and infrared cutoffs

Cosmology of Bianchi type-I metric using renormalization group approach for quantum gravity

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