Off-shell duality in Born–Infeld theory Original Research Article

The classical equations of motion of Maxwell and Born–Infeld theories are known to be invariant under a duality symmetry acting on the field strengths. We implement the SL(2,Z) duality in these theories as linear but non-local transformations on the potentials. We show that the action and the partition function in the Hamiltonian formalism are modular invariant in any gauge. For the Born–Infeld theory we find that the longitudinal part of the fields have to be complexified.