under; with~
Expresses doing something under someone's leadership, influence, or conditions.
の下で literally means 'under' and is used to indicate that an action or situation occurs under a certain authority, guidance, or set of rules. It often appears in formal contexts like reports, announcements, or interviews. You can say you studied under a famous professor, worked under a new policy, or lived under a military regime. The noun before の下で is usually not a physical object but something abstract like a person of authority, an organization, or a principle.