Connector outputs are dust-amount outputs created in commitment transactions specifically to serve as inputs for forfeit transactions. They ensure atomicity of the swap procedure.For each VTXO swap in a commitment transaction, the operator creates a connector output.
The connector output holds a similar tree structure to the batch output, mapping one dust output to each VTXO that requires forfeit protection. It is constructed and owned solely by the Arkade operator.The connector output is meant to be spent in a forfeit transaction to ensure that a swap is conditional on the commitment transaction itself being confirmed onchain.
A connector output is not exclusively for the purpose of a batch swap: it is also used to allow VTXOs to be swapped for an onchain UTXO during an exit.