On Renormalization Group Flows in Four Dimensions

Abstract

We discuss some general aspects of renormalization group flows in four dimensions. Every such flow can be reinterpreted in terms of a spontaneously broken conformal symmetry. We analyze in detail the consequences of trace anomalies for the effective action of the Nambu-Goldstone boson of broken conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly is "non-Abelian," and leads to a positive-definite universal contribution to the S-matrix of 2->2 dilaton scattering. Unitarity of the S-matrix results in a monotonically decreasing function that interpolates between the Euler anomalies in the ultraviolet and the infrared, thereby establishing the a-theorem.

24 pages, 4 figures. v2: references added and minor corrections

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• Broken Scale Invariance and the Regularization of a Conformal Sector in Gravity with Wess-Zumino actions
• Inflation with the Trace Anomaly Action and Primordial Black Holes
• New conformal field theories by gauging electric and magnetic currents
• ${\tau }_{RR}$ minimization in presence of hypermultiplets
• Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows
• Anomalous transport independent of gauge fields
• Softness, Polynomial Boundedness and Amplitudes' Positivity
• Strong gauging or decoupling ghost matter
• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories
• A Light Dilatonic Higgs and a Dilatonic Inflaton in the Georgi-Glashow SU(5) Model
• On the applicability of holography in thermodynamic equilibrium
• Holography and Conformal Anomaly Matching
• EFT of 6D SUSY RG Flows
• Searching for a $C$-function on the three-dimensional sphere
• Monotonicity of RG flow in emergent dual holography of worldsheet nonlinear $\sigma$ model
• Renormalisation group flow of the Jaynes-Cummings model
• Quantum Field Theory on spherical space forms
• Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench
• The Weyl anomaly in interacting quantum field theory on curved spacetimes
• Scale without Conformal Invariance in bottom-up Holography
• Generalized symmetry enriched criticality in (3+1)d
• Boundary Renormalization Group Flow of Entanglement Entropy at a (2+1)-Dimensional Quantum Critical Point
• $c_{\mathrm{eff}}$ from Resurgence at the Stokes Line
• Conformal gauge theory of vector-spinors and spin-3/2 particles
• Series of Tests of a Constraint on Asymptotically Free Gauge Theories
• Entanglement C-functions of defects and interfaces in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• Revisiting the $k$-theorem with the ANEC
• Probing sine dilaton gravity with flow central charge
• Running of the Number of Degrees of Freedom in Quantum Conformal Gravity
• Anomaly-induced vacuum effective action with torsion: covariant solution and ambiguities
• Unitarity and Dilaton effective theory
• Asymptotic safety guaranteed for strongly coupled gauge theories
• Topological Early Universe Cosmology
• Aspects of 4d supersymmetric dynamics and geometry
• Dual RG flows in 4D
• The AdS/CFT partition function, AdS as a lift of a CFT, and holographic RG flow from conformal deformations
• Conformal Windows beyond Asymptotic Freedom
• Entanglement and Excitations in Gauge/Gravity Duality
• Developments in non-relativistic field theory and complexity
• Gradient flows for $\beta$ functions via multi-scale renormalization group equations
• Emergent Supersymmetry in the Marginal Deformations of N=4 SYM
• Cardy's Conjecture and the Spectrum of Infrared Strongly-Coupled Quantum Field Theories
• Renormalization group flow, Entropy and Eigenvalues
• Extended First Law for Entanglement Entropy in Lovelock Gravity
• $\mathcal{N}$ = $1$ Euler Anomaly from RG-dependent metric-Background
• Holographic c-Function
• The a-theorem for the four-dimensional vector model
• The Wasserstein geometry of non-linear sigma models and the Hamilton-Perelman Ricci flow
• Nonlinearly realized conformal invariance in scale invariant field theories
• On the $a$-theorem in the Conformal Window