What psychological or sociological concepts form the basis of Principled Negotiation? Although the various forwards mention that organizational behavior and social psychology are two of the fields that form the basis for the techniques taught at Harvard Law School's Negotiation and Leadership Program, the majority of the material that I've read (Getting to Yes, Getting Past No, Difficult Conversations) tends to frame things in contexts that the average person can easily grasp - romantic relationships, the office environment, and other social conversations.

I want to understand the psychological and sociological underpinnings to this idea, in addition to the application of it (which is covered well in the books I mentioned). However, I'm not sure what exactly terms I should be looking for, and most of my searches are resulting in more business-eqsue style publications.

What concepts can I research to understand the basis of Principled Negotiation and the other communication techniques presented in these works?
That' a very difficult question because research on negotiations is so varied and multidisciplinary. There is prescriptive research stemming from a decision analysis approach and game theory, descriptive research from behavioral economics, and more process-oriented, social-cognitive research. 

As an excellent starting point into psychological research on negotiation I would recommend Leigh Thompson's book:

Thompson, Leigh. 2013. The Mind and the Heart of the Negotiator. Upper Saddle River: Pearson, 6th ed.