The c/a theorem and QFT in curved spacetime

Graham Shore, Swansea University

The c/a theorem is a fundamental result in quantum field theory constraining the nature of renormalization group flows and the relation of UV and IR physics. In the first part of these lectures, we will review early attempts to generalise the 2-dim Zamolodchikov c-theorem to four dimensions, then discuss the 2011 proof of a 4-dim a-theorem by Komargodski and Schwimmer together with recent developments and speculations. In the second part, we will discuss QFT in curved spacetime and show how the background geometry induces a novel analytic structure for Green functions with important consequences for causality, unitarity, dispersion relations and the optical theorem, all of which play a vital role in proving the c/a theorem in flat spacetime.

You can read a nice summary of the current debate on the a-theorem here:

http://www.nature.com/news/proof-found-for-unifying-quantum-principle-1.9352

Approximately 6 hours lectures (tba).