We calculate an effective Polyakov line action of QCD at large N c and large N f from a combined lattice strong coupling and hopping expansion working to second order in both, where the order is defined by the number of windings in the Polyakov line. We compare with the action, truncated at the same order, of continuum QCD on S 1 × S d at weak coupling from one loop perturbation theory, and find that a large N c correspondence of equations of motion found in [1] at leading order, can be extended to the next order. Throughout the paper, we review the background necessary for computing higher order corrections to the lattice effective action, in order to make higher order comparisons more straightforward.

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.

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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.

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.