Quantum measure and Weyl anomaly of two-dimensional bosonic nonlinear σ-models

We define the quantum measure for the bosonic nonlinear σ-model with base space as any compact Riemann surface without boundary. The σ-model is coupled to the background graviton, antisymmetric tensor, and dilaton. Setting up a covariant formalism, we calculate the complete divergent and Weyl-anomalous parts of the 1-loop effective action. This enables us to compare, at the one-loop level, the on-shell and off-shell renormalization groups with the Weyl anomaly. copyright 1988 Academic Press, Inc