Quantum consistency in supersymmetric theories with R-symmetry in curved space

A bstract We discuss consistency at the quantum level in the rigid N N = 1 supersymmetric field theories with a U(1) R symmetry in four-dimensional curved space which are formulated via coupling to the new-minimal supergravity background fields. By analyzing correlation functions of the current operators in the R ℛ -multiplet, we show that the quantum consistency with the (unbroken) supersymmetry requires the U(1) R anomaly coefficient, which depends only on the field content of the theory, to vanish. This consistency condition is obtained under the assumption that the supercurrent Ward identity is non-anomalous and that the vacuum is supersymmetric.