The correct service to use in this scenario is Amazon Cognito, as it provides federated identity management that allows for integration with social identity providers like Facebook, Google, and Amazon, along with SAML and OIDC identity providers. This service simplifies the integration of user authentication through existing social networks within your web application. AWS IAM is a service for managing permissions and is not designed for federated social identity providers. AWS STS provides temporary security credentials for short-term access but not social identity provider integration. AWS Directory Service is used for integrating AWS resources with an existing on-premise Active Directory but is not designed for direct integration with social media identity providers.