What are the applications of such a sidechain, and what are its benefits?
In short, the sidechain allows us to synchronize state transitions and updates across multiple validateers. Being a blockchain, the sidechain can guarantee consistency, ordering of state transition executions, and traceability. We can decentralize a specific business logic and run it on many validateers independently while maintaining state consistency. A further benefit of running multiple validateers is scalability and load-balancing.
This section explains what a sidechain is and how it can be used to enable a coordinated multi-validateer setup.
First some clarification of terminology:
Validateer: Combination of the two terms validator and TEE. A validator in Polkadot is an agent that produces blocks for the blockchain, and TEE is a 'Trusted Execution Environment'. So, a validateer is an agent that produces blocks in a trusted execution environment. This represents a specialization of the more general Integritee 'worker', which does not necessarily incorporate a sidechain.
Sidechain: The sidechain is a blockchain collectively maintained by validateers (i.e. workers that produce sidechain blocks). In the context of Polkadot, this would be a layer 2 blockchain (0 being the relay chain, 1 the 'parent chain' or Parachain).
Parentchain: The layer 1 blockchain that is used by any Integritee worker (including the validateer). When run in the Polkadot ecosystem, this is the Parachain - otherwise, it's a solo chain.