That is probably the PTC line you are refering to, it attaches to the intake air just in front of the turbo and goes all the way to the oil separator box under the intake manifold. Replacement requires removal of the intake manifold.

The other 3 small hoses that go to the turbo are color coded with tape and need to be inspected also. The waste gate actuator is actually above/in front of the turbo but still behind the engine block.

Sounds like it is also time to replace the PCV system, about a 5 hour DIY job. This needs to be done anyway, given the age of the hoses. If left as is, you will soon have more problems than you want: O2 sensor, poor mpg, fouled plugs, new cat, rear main seal, and the list goes on.

Klaus
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Praying for Cynthia Amendt, heaven bound