"CREATE INDEX" Background process in SQL Server
If you are seeing the same index(es) being created over and over again, this is most likely being initiated by the application.  Some applications, particularly reporting or analysis applications, will drop indexes before importing data, and then create them again after the import is complete.

Another possibility is that Automatic index management is enabled.  However, you won't see this creating the same index over and over again, unless something is dropping an index that it creates.

Can you find that index--what table is it on?  I'm wondering now if it might be on a tempdb table that is created, populated, indexed, and dropped repeatedly.

If you can catch it happening with sp_whoisactive that should provide more clues.  Set @show_system_spids = 1.