Tutorial on Scale and Conformal Symmetries in Diverse Dimensions

Abstract

We review the relation between scale and conformal symmetries in various models and dimensions. We present a dimensional reduction from relativistic to non-relativistic conformal dynamics.

Addendum added that includes author S.-H. Ho; Sodano Fest, Perugia, Italy, January 2011

References in corpus (1)

• Weyl Symmetry and the Liouville Theory

Cited by in corpus (37)

• 2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories
• The Renormalization Group and Weyl-invariance
• The Energy-Momentum Tensor(s) in Classical Gauge Theories
• Disk entanglement entropy for a Maxwell field
• Scale without Conformal Invariance: An Example
• The F-Theorem and F-Maximization
• Symmetric Superfluids
• Supercurrent, Supervirial and Superimprovement
• Scale-invariant breaking of conformal symmetry
• Comments on compatibility between Conformal symmetry and Continuous higher-form symmetries
• Scale invariant solids
• Renormalization and conformal invariance of non-local quantum electrodynamics
• From dynamical scaling to local scale-invariance: a tutorial
• Covariant canonical formulations of classical field theories
• Hidden global conformal symmetry without Virasoro extension in theory of elasticity
• Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly
• Comments on Worldsheet Description of the Omega Background
• Comments on scale invariant but non-conformal supersymmetric field theories
• Modular Hamiltonian of the scalar field in the semi infinite line: dimensional reduction for spherically symmetric regions
• On the canonical formulation of gauge field theories and Poincare transformations
• The role of Weyl symmetry in hydrodynamics
• Scale without Conformal Invariance in Dipolar Ferromagnets
• Two-point function of the energy-momentum tensor and generalised conformal structure
• Interacting scale but non-conformal field theories
• Gravity Dual for Cyclic Renormalization Group Flow without Conformal Invariance
• Conserved and non-conserved Noether currents from the quantum effective action
• Kelvin transformation and inverse multipoles in electrostatics
• Scale and Conformal Invariance on (A)dS
• Galilean Electrodynamics: Covariant formulation and Lagrangian
• Geons of Galileons
• Gravity Dual for Hofman-Strominger Theorem
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Vector fields, RG flows and emergent gauge symmetry
• On the non-uniqueness of the energy-momentum and spin currents
• Scale without Conformal Invariance in bottom-up Holography
• Nonlinearly realized conformal invariance in scale invariant field theories
• Extended Conformal Symmetry in $d\ne 4$: Conformal Symmetry of Abelian Gauge Theory in the Physical Sector