Calculating the chiral condensate of QCD at infinite coupling using a generalised lattice diagrammatic approach

We develop a lattice diagrammatic technique for calculating the chiral condensate of QCD at infinite coupling inspired by recent work of Tomboulis and earlier work from the 80's. The technique involves calculating the contribution of gauge link diagrams formed from all possible combinations of a truncated number of sub-diagram types, by performing a resummation. We show how to calculate the relevant sub-diagrams, including a new technique for evaluating group integrals with arbitrary number of gauge link elements, using Young Projectors. Including up to four different diagram types we calculate the chiral condensate as a function of N-f, and show that two real solutions result, which are non-zero for all integer N-f. We analyse these solutions and find signs of convergence of the expansion at small N-f. We should stress that a drawback of our technique is that, due to the addition of non-tree diagrams in the resummation, there are sources of error associated with miscounting and over-counting of diagrams. We discuss these sources of error in detail, and implement a technique to reduce over-counting of diagrams, while leaving other sources of error for future work.