Vector Induced Lattice Gauge Theories

We consider vector induced lattice gauge theories, in particular we consider the QED induced and we show that at negative temperature corresponds to the dimer problem while at positive temperature it describes a gas of branched polymers with loops. We show that the fermionic models have D_c = 6 as upper critical dimension for N ≠ ∞ while the N = ∞ model has no upper critical dimension. We also show that the bosonic models without potential are not critical in the range of stability of the integral definition of the partition function but they behave as the fermionic models when we analytically continue the free energy.