Galilean Yang-Mills Theory

Abstract

We investigate the symmetry structure of the non-relativistic limit of Yang-Mills theories. Generalising previous results in the Galilean limit of electrodynamics, we discover that for Yang-Mills theories there are a variety of limits inside the Galilean regime. We first explicitly work with the $SU(2)$ theory and then generalise to $SU(N)$ for all $N$, systematising our notation and analysis. We discover that the whole family of limits lead to different sectors of Galilean Yang-Mills theories and the equations of motion in each sector exhibit hitherto undiscovered infinite dimensional symmetries, viz. infinite Galilean Conformal symmetries in $D=4$. These provide the first examples of interacting Galilean Conformal Field Theories (GCFTs) in $D>2$.

35 pages

References in corpus (14)

• 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
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• Flat-Space Chiral Gravity
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• Galilean Conformal Electrodynamics
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Cited by in corpus (18)

• Flat Holography: Aspects of the dual field theory
• Field Theories with Conformal Carrollian Symmetry
• Extended Galilean symmetries of non-relativistic strings
• Tensionless Superstrings: View from the Worldsheet
• The nuts and bolts of the BMS Bootstrap
• Interacting Conformal Carrollian Theories: Cues from Electrodynamics
• Inhomogeneous Tensionless Superstrings
• Dynamical structure of Carrollian Electrodynamics
• Aspects of Non-Relativistic Quantum Field Theories
• Galilean Gauge Theories from Null Reductions
• Note About Hamiltonian Formalism for Newton-Cartan String and p-Brane
• Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure
• Flatspace Chiral Supergravity
• Constructing Non-Relativistic AdS${}_5$/CFT${}_4$ Holography
• Recent developments of the Lauricella string scattering amplitudes and their exact SL(K+3,C) Symmetry
• Galilean fermions: Classical and quantum aspects
• Symmetries and Couplings of Non-Relativistic Electrodynamics
• From $\mathcal{N}=4$ Galilean superparticle to three-dimensional non-relativistic $\mathcal{N}=4$ superfields