A Change of Variables to the Dual and Factorization of Composite Anomalous Jacobians

TL;DR

This paper develops explicit variable transformations for sigma-model duals, calculates related Jacobians, and proposes rules to factorize anomalies in composite Jacobians across different algebraic structures.

Contribution

It introduces explicit change-of-variable constructions for dual models and generalizes anomaly factorization rules for composite Jacobians in various algebraic contexts.

Findings

Explicit Jacobian calculations for dual sigma-models.

Proposed rules for anomaly factorization in composite Jacobians.

Formulas for anomalies in semisimple and solvable algebras.

Abstract

Changes of variables giving the dual model are constructed explicitly for sigma-models without isotropy. In particular, the jacobian is calculated to give the known results. The global aspects of the abelian case as well as some of those of the cases where the isometry group is simply connected are considered. Considering the anomalous case, we infer by a consistency argument that the `multiplicative anomaly' should be replaceable by adequate rules for factorization of composite jacobians. These rules are then generalized in a simple way for composite jacobians defined in spaces of different types. Implimentation of these rules then gives specific formulas for the anomally for semisimple algebras and also for solvable ones.