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For the Windows service, the only requirements for the service account are (assuming default file system package store configuration) read/write access to the directory where the underlying packages are stored (default is in ProgramData), read/write access to the service installation directory (default is in Program Files), and granted access to the ProGet database role named ProGetUser_Role.
For the web application (Windows service or IIS application pool identity), the requirements are the same as the Windows service, plus read/write access to the website installation directory.
Note again that the Desktop Hub installation privileges is orthogonal to the account that ProGet runs as, since it would obviously require more privilege to create/update/grant in the database and also create subfolders in Program Files & %ProgramData%. As an extra word of caution, if D: is a mapped drive, be sure to use the full UNC path in configuration settings within ProGet.