Chiral Lagrangians, Anomalies, Supersymmetry, and Holomorphy

TL;DR

This paper explores higher-dimensional analogues of 2D chiral systems, revealing their connections to anomalies, supersymmetry, and holomorphic structures, and demonstrating their role in inducing generalized chiral algebras and supersymmetric theories.

Contribution

It introduces higher-dimensional $bc$ systems coupled to gauge fields, generalizes chiral algebras to $2n$ dimensions, and links these systems to supersymmetric matter and self-dual theories.

Findings

Explicit evaluation of $bc$ partition functions using anomalies and holomorphy.

Generalization of 2D chiral algebras to $2n$ dimensions.

Connection of $bc$ systems to supersymmetric theories and self-dual fields.

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 $WZW_4$ theory, as defined by Losev et. al., and the classical open $\mathcal{N}_{ws}=2$ string.