WZW in the lightlike directions

Dimensional reduction of the M5 brane on a Lorentzian manifold along a lightlike direction results in a five-dimensional gauge theory, which can be reformulated covariantly in six dimensions, where one puts the Lie derivatives along the lightlike direction of all fields to zero as constraints. Without imposing these constraints, we have a nonsupersymmetric six-dimensional gauge theory that we may expect shall have a six dimensional gauge symmetry. However this gauge symmetry has an anomaly for certain Lorentzian six-manifolds. We show that this gauge anomaly can be canceled by adding a WZW theory in the 2d space that is spanned by two lightlike directions.