String from Large N Gauge Fields via Graph Summation on a $P^{+} - x^{+}$ Lattice

I describe renewed efforts to establish a string description of large N_c QCD by summing large ``fishnet'' diagrams. Earlier work on fishnets indicated that the usual relativistic (zero thickness) string theory can arise at strong 't Hooft coupling, at best yielding a highly idealized description, which fails to incorporate such salient features of continuum QCD as asymptotic freedom and point-like constituents. The recently conjectured AdS/CFT correspondence is compatible with such limitations because it also gives a simple picture of large N_c gauge theory only at strong coupling. In order to better understand how string theory could emerge from large N_c QCD at strong coupling, Klaus Bering, Joel Rozowsky, and I have developed an improved implementation of my effort of the late seventies to digitize the planar diagrams of large N_c light-cone quantized QCD by discretizing both P+ and x+. This discretization allows a strong coupling limit of the sum of planar diagrams to be defined and studied. It also provides a natural framework to explore the possible dual relationship between QCD in light-cone gauge and string theory quantized on the light-cone