Calculating the chiral condensate diagrammatically at strong coupling

Abstract

We calculate the chiral condensate of QCD at infinite coupling as a function of the number of fundamental fermion flavours using a lattice diagrammatic approach inspired by recent work of Tomboulis, and other work from the 80's. We outline the approach where the diagrams are formed by combining a truncated number of sub-diagram types in all possible ways. Our results show evidence of convergence and agreement with simulation results at small N f . However, contrary to recent simulation results, we do not observe a transition at a critical value of N f . We further present preliminary results for the chiral condensate of QCD with symmetric or adjoint representation fermions as a function of N f for N c = 3. In general, there are sources of error in this approach associated with miscounting of overlapping diagrams, and over-counting of diagrams due to symmetries. These are further elaborated upon in a longer paper.