Abstract
We construct the free Lagrangian of the magnetic sector of Carrollian electrodynamics. The construction relies on Helmholtz integrability condition for differential equations in a self-consistent algorithm, working hand in hand with imposing invariance under infinite dimensional Conformal Carroll algebra. It requires inclusion of new fields in the dynamics and the system is free of gauge redundancies. We next add interaction (quartic) terms to the free Lagrangian, strictly constrained by conformal invariance and Carrollian symmetry. The dynamical realization of the non-semi-simple infinite dimensional symmetry algebra at the level of charge algebra is exact and free from central terms.
Highlights
Symmetry principles play an extremely crucial role in building models describing fundamental particles and interactions
On the other hand, organizing the space of quantum field theories (QFTs) by classification of conformal field theories (CFTs) is an alluring yet extremely challenging umbrella program. This overall wisdom is guided by the age old Wilsonian point of view, which supposedly should dictate whether a certain QFT can flow to a CFT via a relevant deformation
II, we briefly review the infinite dimensional conformal Carrollian algebra and how the generators of the algebra acts on fields
Summary
Symmetry principles play an extremely crucial role in building models describing fundamental particles and interactions. Since conformal Carroll isometries act locally in real space, it sheds an interesting possibility of finding interacting theories with infinite dimensional symmetry group. This led some of the present authors to an ambitious program of looking into Carrollian field theories. The most important feature of this example is that it is an interacting theory invariant under the infinite dimensional conformal Carroll isometry group Curiously, this does not descend either at the level of action, or at the level of equations of motion, as an ultrarelativistic limit of a relativistic field theory
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