Galilean Field Theories and Conformal Structure

Abstract

We perform a detailed analysis of Galilean field theories, starting with free theories and then interacting theories. We consider non-relativistic versions of massless scalar and Dirac field theories before we go on to review our previous construction of Galilean Electrodynamics and Galilean Yang-Mills theory. We show that in all these cases, the field theories exhibit non-relativistic conformal structure (in appropriate dimensions). The surprising aspect of the analysis is that the non-relativistic conformal structure exhibited by these theories, unlike relativistic conformal invariance, becomes infinite dimensional even in spacetime dimensions greater than two. We then couple matter with Galilean gauge theories and show that there is a myriad of different sectors that arise in the non-relativistic limit from the parent relativistic theories. In every case, if the parent relativistic theory exhibited conformal invariance, we find an infinitely enhanced Galilean conformal invariance in the non-relativistic case. This leads us to suggest that infinite enhancement of symmetries in the non-relativistic limit is a generic feature of conformal field theories in any dimension.

47 pages, 4 figures

References in corpus (13)

• The BMS/GCA correspondence
• Conformal Carroll groups and BMS symmetry
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Galilean Conformal Algebras and AdS/CFT
• Flat Holography: Aspects of the dual field theory
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Entanglement entropy in Galilean conformal field theories and flat holography
• Flat-Space Chiral Gravity
• The BMS Bootstrap
• Galilean Superconformal Symmetries
• Galilean Conformal Electrodynamics
• The nuts and bolts of the BMS Bootstrap
• Overview of Non-Relativistic QCD

Cited by in corpus (16)

• Field Theories with Conformal Carrollian Symmetry
• A Tale of Three. Tensionless strings and vacuum structure
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• Interacting Conformal Carrollian Theories: Cues from Electrodynamics
• Local quantum energy conditions in non-Lorentz-invariant quantum field theories
• Non-Lorentzian Chaos and Cosmological Holography
• Galilean Gauge Theories from Null Reductions
• Schrödinger symmetry: a historical review
• The Shadow Formalism of Galilean CFT${}_2$
• Carrollian Yang-Mills Theory
• Quantization of Interacting Galilean Field theories
• BMS Modular Diaries: Torus one-point function
• Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure
• Galilean Electrodynamics: Covariant formulation and Lagrangian
• Galilean fermions: Classical and quantum aspects
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications