Left shoulder mri arthrogram- report states that sgh ligament is not seen. does this mean it is completely torn? will surgery be necessary?

Not visualized: "not seen likely means "not visualized", so can't tell whether intact or not. You should follow-up with your surgeon to see if surgery is needed- if visualization of the sgh is the main clinical question, you may need arthroscopy to visualize it.

We treat the patient: Not the pictures. You need to ask the surgeon (orthopedic doctor) what they think about this finding (or non finding as explained in the prior answer) the study might not have been done with sufficient resolution to see this ligament. And you can also ask the radiologist who did the study what they think. This requires some more thought.

Depends: The SGHL is normally absent in about 10 percent of patients, so it may be torn or a normal variant. Additional findings of injury to the biceps tendon with subluxation, accompanied by pain with certain motions such as baseball throwing, will determine whether surgery is indicated. Surgery also depends on the patient's career and life style. Consultation with you Orthopedic Surgeon is recommended.