A global index, by very definition, is a single index on the parent table that maps to many underlying table partitions. The parent table itself does not have a single, unified underlying store so it must, therefore, retrieve the data satisfying index constraints from physically distributed tables. In very crude terms, the global index accumulates [&]

https://www.percona.com/blog/2019/11/20/proposal-for-global-indexes-in-postgresql/