Self-duality for interacting fields

The authors determine the supersymmetric coupling of chiral N = 4b supergravity in six dimensions to an arbitrary number n of anti-self-dual tensor multiplets. In a novel phenomenon, the five self-duality and n anti-self-duality conditions for the two-index tensors are modified by the scalar interactions to be non-diagonal in terms of the elementary tensor gauge fields, which transform irreducibly under a global SO(5, n) invariance. The 5n scalar fields parametrize the coset manifold SO(5, n)/[SO(5) x SO(n)]. The truncated N = 2 systems, in which the n scalars parametrize the space SO(n, 1)/SO(n), are derived and found to have analogous properties. In general the theories do not admit action principles possessing manifest linearly realized Lorentz invariance, so the construction is effected at the level of the supersymmetry transformations and field equations. The authors speculate on generalizations including N = 2 vector matter, and comment on the possible implications of our results for chiral superstring models