We investigate higher-dimensional analogues of the bc systems of 2D RCFT. When coupled to gauge fields and Beltrami differentials defining integrable holomorphic structures, the bc partition functions can be explicitly evaluated using anomalies and holomorphy. The resulting induced actions generalize the chiral algebras of 2D RCFT to 2n dimensions. Moreover, bc systems in four and six dimensions are closely related to supersymmetric matter. In particular, we show that d = 4, script N = 2 hypermultiplets induce a theory of self-dual Yang-Mills fields coupled to self-dual gravity. In this way the bc systems fermionize both the algebraic sector of the WZW4 theory, as defined by Losev et al., and the classical open script NWS = 2 string.