AKHILA MOHAN

We investigate the existence of action for both the electric and magnetic sectors of Galilean Electrodynamics using Helmholtz conditions. We prove the existence of unique action in magnetic limit with the addition of a scalar field in the system. The check also implies the non existence of action in the electric sector of Galilean electrodynamics. Dirac constraint analysis of the theory reveals that there are no local degrees of freedom in the system. Further, the theory enjoys a reduced but an infinite dimensional subalgebra of Galilean conformal symmetry algebra as global symmetries. The full Galilean conformal algebra however is realized as canonical symmetries on the phase space. The corresponding algebra of Hamilton functions acquire a state dependent central charge.

We construct an [Formula: see text] supersymmetric gauge theory in Lifshitz space–time. Starting with [Formula: see text] supersymmetric Lagrangian, we introduce an additional [Formula: see text] symmetry between specific component fields. The resultant Lagrangian is shown to have an extra set of supersymmetry, thus realizing an on-shell [Formula: see text] supersymmetric gauge theory. Just as in the case of [Formula: see text], the superderivatives and superfields involved contain higher-order derivatives of spatial coordinates. The constructed [Formula: see text] supersymmetric Lagrangian has both vector multiplet and hypermultiplet.

We construct the free Lagrangian of the magnetic sector of Carrollian electrodynamics, which surprisingly, is not obtainable as an ultra-relativistic limit of Maxwellian 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 (CCA). It requires inclusion of new fields in the dynamics and the system in free of gauge redundancies. We calculate two-point functions in the free theory based entirely on symmetry principles. We next add interaction (quartic) terms to the free Lagrangian, strictly constrained by conformal invariance and Carrollian symmetry. Finally, a successful dynamical realization of infinite dimensional CCA is presented at the level of charges, for the interacting theory. In conclusion, we calculate the Poisson brackets for these charges.