Coupling Chiral Bosons to Gravity

The chiral boson actions of Floreanini and Jackiw (FJ), and of McClain, Wu and Yu (MWY) have recently been shown to be different representations of the same chiral boson theory. MWY displays manifest covariance and also a (gauge) symmetry that is hidden in the FJ side, which, on the other hand, displays the physical spectrum in a simpler manner. We make use of the manifest covariance of the MWY chiral boson representation to couple it to background gravity showing explicitly the equivalence with the previous results for the FJ representation.