The role of instantons in scale-invariant gauge theories

1980 ◽  
Vol 171 ◽  
pp. 420-444 ◽  
Author(s):  
Ian Affleck
Keyword(s):  
Gauge Theories ◽  
Scale Invariant ◽  
Invariant Gauge

scholarly journals Holographic models of composite Higgs in the Veneziano limit. Part I. Bosonic sector

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Daniel Elander ◽  
Michele Frigerio ◽  
Marc Knecht ◽  
Jean-Loïc Kneur
Keyword(s):  
Symmetry Breaking ◽  
Gauge Theories ◽  
Scale Invariant ◽  
Strongly Coupled ◽  
Mass Gap ◽  
Composite Higgs ◽  
Holographic Approach ◽  
Scaling Dimension ◽  
Invariant Gauge ◽  
Domain Of Validity

Abstract We study strongly-coupled, approximately scale-invariant gauge theories, which develop a mass gap in the infrared. We argue that a large number of fermion flavours is most suitable to provide an ultraviolet completion for the composite Higgs scenario. The holographic approach allows to describe the qualitative features of the non-perturbative dynamics in the Veneziano limit. We introduce new bottom-up holographic models, which incorporate the backreaction of flavour on the geometry, and show that this can correlate the mass gap to the scale of flavour-symmetry breaking. We compute the mass spectrum for the various composite bosonic states, and study its dependence on the scaling dimension of the symmetry-breaking operators, as well as on the number of flavours. The different regions with a light dilaton are critically surveyed. We carefully assess the domain of validity of the holographic approach, and compare it with lattice simulations and the Nambu-Jona-Lasinio model.

scholarly journals Omega vs. pi, and 6d anomaly cancellation

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Joe Davighi ◽  
Nakarin Lohitsiri
Keyword(s):  
Gauge Theories ◽  
Necessary Conditions ◽  
Homotopy Groups ◽  
Mapping Torus ◽  
Anomaly Cancellation ◽  
Global Anomaly ◽  
Gauge Anomalies ◽  
Local Anomalies ◽  
Dimensional Mapping

Abstract In this note we review the role of homotopy groups in determining non-perturbative (henceforth ‘global’) gauge anomalies, in light of recent progress understanding global anomalies using bordism. We explain why non-vanishing of πd(G) is neither a necessary nor a sufficient condition for there being a possible global anomaly in a d-dimensional chiral gauge theory with gauge group G. To showcase the failure of sufficiency, we revisit ‘global anomalies’ that have been previously studied in 6d gauge theories with G = SU(2), SU(3), or G2. Even though π6(G) ≠ 0, the bordism groups $$ {\Omega}_7^{\mathrm{Spin}}(BG) $$ Ω 7 Spin BG vanish in all three cases, implying there are no global anomalies. In the case of G = SU(2) we carefully scrutinize the role of homotopy, and explain why any 7-dimensional mapping torus must be trivial from the bordism perspective. In all these 6d examples, the conditions previously thought to be necessary for global anomaly cancellation are in fact necessary conditions for the local anomalies to vanish.

scholarly journals In search of a pristine signal for (scale-)chiral symmetry in nuclei

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740023 ◽  
Author(s):  
Mannque Rho
Keyword(s):  
Chiral Symmetry ◽  
Nuclear Physics ◽  
Local Symmetry ◽  
Point Interaction ◽  
Strongly Correlated ◽  
Scale Invariant ◽  
Unpublished Note ◽  
Nuclear Interactions ◽  
Vector Formula

I describe the long-standing search for a “smoking-gun” signal for the manifestation of (scale-)chiral symmetry in nuclear interactions. It is prompted by Gerry Brown’s last unpublished note, reproduced verbatim below, on the preeminent role of pions and vector ([Formula: see text]) mesons in providing a simple and elegant description of strongly correlated nuclear interactions. In this note written in tribute to Gerry Brown, I first describe a case of an unambiguous signal in axial-charge transitions in nuclei and then combine his ideas with the more recent development on the role of hidden symmetries in nuclear physics. What transpires is the surprising conclusion that the Landau–Migdal fixed point interaction [Formula: see text], the nuclear tensor forces and Brown–Rho scaling, all encoded in scale-invariant hidden local symmetry, as Gerry put, “run the show and make all forces equal.”

Scale-invariant Characteristics of Forgetting: Toward a Unifying Account of Hippocampal Forgetting across Short and Long Timescales

2020 ◽  
Vol 32 (3) ◽  
pp. 386-402
Author(s):  
Talya Sadeh ◽  
Yoni Pertzov
Keyword(s):  
Time Dependent ◽  
Scale Invariant ◽  
Relational Information ◽  
Recent Advances ◽  
Growing Body ◽  
Neural Underpinnings ◽  
Important Extension ◽  
Long Timescales ◽  
Prevailing View

After over 100 years of relative silence in the cognitive literature, recent advances in the study of the neural underpinnings of memory—specifically, the hippocampus—have led to a resurgence of interest in the topic of forgetting. This review draws a theoretically driven picture of the effects of time on forgetting of hippocampus-dependent memories. We review evidence indicating that time-dependent forgetting across short and long timescales is reflected in progressive degradation of hippocampal-dependent relational information. This evidence provides an important extension to a growing body of research accumulated in recent years, showing that—in contrast to the once prevailing view that the hippocampus is exclusively involved in memory and forgetting over long timescales—the role of the hippocampus also extends to memory and forgetting over short timescales. Thus, we maintain that similar rules govern not only remembering but also forgetting of hippocampus-dependent information over short and long timescales.

scholarly journals Broadband Microwave Absorption by Logarithmic Spiral Metasurface

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Shubo Wang ◽  
Bo Hou ◽  
Che Ting Chan
Keyword(s):  
Electromagnetic Wave ◽  
Scale Invariance ◽  
Logarithmic Spiral ◽  
Unit Cell ◽  
Scale Invariant ◽  
Archimedean Spiral ◽  
Broadband Absorption ◽  
Fabry Perot ◽  
Classical Waves

Abstract Metamaterials have enabled the design of electromagnetic wave absorbers with unprecedented performance. Conventional metamaterial absorbers usually employ multiple structure components in one unit cell to achieve broadband absorption. Here, a simple metasurface microwave absorber is proposed that has one metal-backed logarithmic spiral resonator as the unit cell. It can absorb >95% of normally incident microwave energy within the frequency range of 6 GHz–37 GHz as a result of the scale invariant geometry and the Fabry-Perot-type resonances of the resonator. The thickness of the metasurface is 5 mm and approaches the Rozanov limit of an optimal absorber. The physics underlying the broadband absorption is discussed. A comparison with Archimedean spiral metasurface is conducted to uncover the crucial role of scale invariance. The study opens a new direction of electromagnetic wave absorption by employing the scale invariance of Maxwell equations and may also be applied to the absorption of other classical waves such as sound.

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