Brian Greene is a fantastic presenter and accomplished theoretical physicist. I often refer my physics students to his popular books. In physics itself his achievements are largely in the area of string theory where he has made a name for himself with his work on Calabi-Yau manifolds and topology.
The challenge for Greene and other physicists involved in string theory is that at this stage it remains a largely theoretical (albeit mathematically attractive) endeavour that awaits a great deal of empirical verification. Until that happens a Nobel Prize in Physics is unlikely to be granted in this realm. It is the same problem that faces Edward Witten (founder of M-theory), Leonard Susskind and other pioneers in string theory.
Witten to his credit though was awarded a Fields Medal in 1990. If a Nobel for String Theory is ever awarded he is a far more likely candidate than Greene to receive it.
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