  It is frequently useful to construct dual descriptions of theories containing
antisymmetric tensor fields by introducing a new potential whose curl gives the
dual field strength, thereby interchanging field equations with Bianchi
identities. We describe a general procedure for constructing actions containing
both potentials at the same time, such that the dual relationship of the field
strengths arises as an equation of motion. The price for doing this is the
sacrifice of manifest Lorentz invariance or general coordinate invariance,
though both symmetries can be realized nonetheless. There are various examples
of global symmetries that have been realized as symmetries of field equations
but not actions. These can be elevated to symmetries of the action by our
method. The main example that we focus on is the low-energy effective action
description of the heterotic string theory compactified on a six-torus to four
dimensions. We show that the SL(2,R) symmetry, whose SL(2,Z) subgroup has been
conjectured to be an exact symmetry of the full string theory, can be realized
on the action in a way that brings out a remarkable similarity to the target
space duality symmetry O(6,22). Our analysis indicates that SL(2,Z) symmetry
may arise naturally in a dual formulation of the theory.
