SL(2,R) duality-symmetric action for electromagnetic theory with electric and magnetic sources

•We formulate a local, manifestly duality-symmetric, Zwanziger-type action.•Maxwell electrodynamics is generalized to include dilaton and axion fields.•SL(2,R) symmetry is manifest.•We formulate a local, manifestly duality-symmetric, nonlinear Born–Infeld action with SL(2,R) symmetry.

For the SL(2,R) duality-invariant generalization of Maxwell electrodynamics in the presence of both electric and magnetic sources, we formulate a local, manifestly duality-symmetric, Zwanziger-type action by introducing a pair of four-potentials AμAμ and BμBμ in a judicious way. On the two potentials AμAμ and BμBμ the SL(2,R) duality transformation acts in a simple linear manner. In quantum theory including charged source fields, this action can be recast as a SL(2,Z)-invariant action. Also given is a Zwanziger-type action for SL(2,R) duality-invariant Born–Infeld electrodynamics which can be important for D-brane dynamics in string theory.