Walnut, also referred to as just Nut by his associates, was an antagonist in Doctor Sleep, and main doctor to The True Knot. His rube name was Peter Wallis, and he was from Little Rock, Arkansas.
During Andi's initiation into the True Knot, he didn't think she would survive. It is also stated that his own initiation was in front of a bonfire, rather than a circle of headlights.
After Grampa Flick dies, he theorized that the True were becoming sick, with colds and eventually the measles, due to bad steam from the kid they fed off of in Iowa, Bradley Trevor, was sick or carrying the disease. It was dormant in all the members of the True, coming out now due to malnutrition or stress. He also figured that if Abra Stone had been vaccinated, her steam could help protect them.