Superpotentials for Gauge and Conformal Supergravity Backgrounds

TL;DR

This paper derives quantum-corrected effective superpotentials for super Yang-Mills and conformal supergravity backgrounds in N=1 SUSY theories, showing that conformal flatness is preserved by quantum effects.

Contribution

It provides explicit forms of quantum corrections to superpotentials in supergravity backgrounds, extending Veneziano-Yankielowicz terms to include matter fields in fundamental representations.

Findings

Quantum corrections to superpotentials are derived.

Background conformal flatness remains unchanged by quantum effects.

Results generalize known superpotential forms to supergravity contexts.

Abstract

Effective superpotentials obtained by integrating out matter in super Yang-Mills and conformal supergravity backgrounds in N=1 SUSY theories are considered. The pure gauge and supergravity contributions (generalizing Veneziano-Yankielowicz terms) are derived by considering the case with matter fields in the fundamental representation of the gauge group. These contributions represent quantum corrections to the tree-level Yang-Mills and conformal supergravity actions. The classical equations of motion following from the conformal supergravity action require the background to be (super)conformally flat. This condition is unchanged by quantum corrections to the effective superpotential, irrespective of the matter content of the theory.