The 4D-2D projection of Lorentz-violating Myers-Pospelov QED

We consider the four-dimensional quantum electrodynamics extended with Myers-Pospelov Lorentz-violating dimension-5 operators to investigate 4D-2D projection. In projecting out the 4D theory down to a 2D theory we get analogs of these operators. Namely, we obtain a new two-dimensional theory with corresponding scalar and fermionic 2D Myers-Pospelov Lorentz-violating dimension-3 operators. New defect structures can also be found from this new projected out 2D scalar sector. Furthermore, we also show that this 2D scalar sector can be also radiatively induced through the new 2D fermionic sector.