Comprehensive and Detailed In-Depth Explanation:

Periodic Service Tokens allow renewal without changing the token, addressing the application’s issue. The Vault documentation states:

"In some cases, having a token be revoked would be problematic -- for instance, if a long-running service needs to maintain its SQL connection pool over a long period of time. In this scenario, a periodic token can be used. The idea behind periodic tokens is that it is easy for systems and services to perform an action relatively frequently -- for instance, every two hours, or even every five minutes. Therefore, as long as a system is actively renewing this token -- in other words, as long as the system is alive -- the system is allowed to keep using the token and any associated leases."

—Vault Concepts: Tokens

A: Correct. Periodic tokens maintain stability with renewal:

"A Periodic Service Token is a type of token in Vault that can be renewed periodically without the need for the application to re-authenticate every time the token changes."

—Vault Concepts: Tokens

B: Root tokens are insecure for applications due to unlimited access:

"Root tokens should not be used for application authentication due to their high level of access and security risks."

—Vault Concepts: Tokens

C: Orphan tokens don’t support periodic renewal inherently.

D: Batch tokens cannot be renewed:

"Batch tokens cannot be renewed."

—Vault Tutorials: Batch Tokens