Chiral Lagrangians, Anomalies, Supersymmetry, and Holomorphy

Abstract

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 $d=4,\mathcal{N}=2$ 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 $WZ{W}_4$ theory, as defined by Losev et. al., and the classical open ${\mathcal{N}}_{ws}=2$ string.

31 pp., Harvmac (b) mode

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