Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching

Abstract

We argue that when conformal symmetry is spontaneously broken the trace anomalies in the broken and unbroken phases are matched. This puts strong constraints on the various couplings of the dilaton. Using the uniqueness of the effective action for the Goldstone supermultiplet for broken $\mathcal{N}=1$ superconformal symmetry the dilaton effective action is calculated.

arXiv comment29 pages, 2 figures

References in corpus (10)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• The Exact Superconformal R-Symmetry Maximizes a
• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions
• The one-loop effective action and trace anomaly in four dimensions
• Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
• Closed Form Effective Conformal Anomaly Actions in D$\ge$4
• Exact Consequences of the Trace Anomaly in Four Dimensions
• Conformal Anomalies -- Recent Progress

Cited by in corpus (82)

• On Renormalization Group Flows in Four Dimensions
• The Constraints of Conformal Symmetry on RG Flows
• Comments on Holographic Entanglement Entropy and RG Flows
• The Effective Theory of Long Strings
• A Constraint on Defect and Boundary Renormalization Group Flows
• On renormalization group flows and the a-theorem in 6d
• Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories
• Low-energy effective action for pions and a dilatonic meson
• A naturally light dilaton
• 5D Rotating Black Holes and the nAdS${}_2$/nCFT${}_1$ Correspondence
• Universal Entanglement and Boundary Geometry in Conformal Field Theory
• Renormalised 3-point functions of stress tensors and conserved currents in CFT
• On the Large $R$-charge Expansion in $\mathcal{N}=2$ Superconformal Field Theories
• New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order
• Universal correlation functions in rank 1 SCFTs
• Supersymmetry on curved spaces and superconformal anomalies
• Spin Impurities, Wilson Lines and Semiclassics
• TTT in CFT: Trace Identities and the Conformal Anomaly Effective Action
• RG flows in d dimensions, the dilaton effective action, and the a-theorem
• Weyl Charges in Asymptotically Locally AdS${}_3$ Spacetimes
• Exploring soft constraints on effective actions
• The Conformal Anomaly of M5-Branes
• Universal Asymptotics for High Energy CFT Data
• Super-Weyl anomalies in N=2 supergravity and (non)local effective actions
• Defect $a$-Theorem and $a$-Maximization
• General approach to the Lagrangian ambiguity in $f(R,T)$ gravity
• Double-soft behavior of the dilaton of spontaneously broken conformal invariance
• Consistency of local renormalization group in d=3
• Superconformal duality-invariant models and $\mathcal{N}=4$ SYM effective action
• The holographic dilaton
• Scale invariance vs conformal invariance
• General anomaly matching by Goldstone bosons
• Conjecture on Hidden Superconformal Symmetry of N=4 Supergravity
• On c-theorems in arbitrary dimensions
• Bootstrapping the $a$-anomaly in $4d$ QFTs
• Perturbative c-theorem in d-dimensions
• The a-theorem and conformal symmetry breaking in holographic RG flows
• Conformal Anomalies in Hydrodynamics
• Shining Flavor and Radion Phenomenology in Warped Extra Dimension
• Conformal Anomalies and Gravitational Waves
• Supervertices and Non-renormalization Conditions in Maximal Supergravity Theories
• A functional RG equation for the c-function
• Nonlocal action for the super-Weyl anomalies: A new representation
• Fermi Condensation induced by Weyl Anomaly
• Conformal Anomaly for Non-Conformal Scalar Fields
• Comments on Anomalies in Supersymmetric Theories
• Type-B Anomaly Matching and the 6D (2,0) Theory
• All the entropies on the light-cone
• On Wald entropy of black holes: logarithmic corrections and trace anomaly
• The Dilaton Wess-Zumino Action in 6 Dimensions from Weyl Gauging: Local Anomalies and Trace Relations
• (Mis-)Matching Type-B Anomalies on the Higgs Branch
• Superconformal Sum Rules and the Spectral Density Flow of the Composite Dilaton (ADD) Multiplet in $\mathcal{N}=1$ Theories
• Non-compact duality, super-Weyl invariance and effective actions
• Weyl Anomaly induced Fermi Condensation and Holography
• Thermal power spectrum in the CFT driven cosmology
• Infrared behavior of Weyl Gravity: Functional Renormalization Group approach
• Early universe in quantum gravity
• (Delta a) curiosities in some 4d susy RG flows
• Spontaneous Breaking of Non-Relativistic Scale Symmetry
• The dilaton Wess-Zumino action in higher dimensions
• A rederivation of the conformal anomaly for spin-1/2
• Dilaton Effective Action with $\mathcal{N}=1$ Supersymmetry
• $a$-Anomalous Interactions of the Holographic Dilaton
• Renormalization Group Flows, the $a$-Theorem and Conformal Bootstrap
• Dark side of Weyl gravity
• Conformal anomalies and the Einstein Field Equations
• Chiral current induced by torsional Weyl anomaly
• Superconformal anomalies from superconformal Chern-Simons polynomials
• Trace Anomaly Matching and Exact Results For Entanglement Entropy
• Covariantly Constant Anomalies on Conformal Manifolds
• Comments on the Algebraic Properties of Dilaton Actions
• Dilatons Improve (Non)-Goldstones
• $\mathcal{N}=1$ Euler Anomaly Flow from Dilaton Effective Action
• Dilaton in scalar QFT: a no-go theorem in $4-\epsilon$ and $3-\epsilon$ dimensions
• Note On The Dilaton Effective Action And Entanglement Entropy
• Superspace formulation of the local RG equation
• The a-theorem for the four-dimensional gauged vector model
• EFT of 6D SUSY RG Flows
• Holography and Conformal Anomaly Matching
• Aspects of 4d supersymmetric dynamics and geometry
• The a-theorem for the four-dimensional vector model
• $\mathcal{N}$ = $1$ Euler Anomaly from RG-dependent metric-Background