QFT Colloquia Day with John Gracey and Radu Roiban

We report on recent work in relation to properties of conformal field theories in spacetime dimensions d > 2. The presentation is in two parts where the focus in the first is on scalar cubic theories which are studied in relation to the Lee-Yang model and percolation theory. Estimates of critical exponents at the Wilson-Fisher fixed point derived from Schnetz’s six loop renormalization are produced. Applying resummation methods the exponent estimates are in good agreement with estimates from other methods such as Monte Carlo, high T_c expansions, functional renormalization group and the conformal bootstrap. The second part concentrates on nonabelian gauge theories and in particular the Banks-Zaks-Caswell (BZC) fixed point in four dimensions which defines the conformal window. Using the BZC expansion we compute several critical exponents to fourth order for SU(3) producing estimates which, with a suitable resummation, are in reasonable agreement with lattice field theory across the full conformal window. An estimate of the location of the lower conformal window boundary is indicated and compared with those from other methods. The situation with other colour groups and quark representations is also discussed.