Non-String Pursuit towards Unified Model on the Lattice

Non-standard overview on the possible formulation towards a unified model onthe lattice is presented. It is based on the generalized gauge theory which isformulated by differential forms and thus expected to fit in a simplicialmanifold. We first review suggestive known results towards this direction. As asmall step of concrete realization of the program, we propose a latticeChern-Simons gravity theory which leads to the Chern-Simons gravity in thecontinuum limit via Ponzano-Regge model. We then summarize the quantizationprocedure of the generalized gauge theory and apply the formulation to thegeneralized topological Yang-Mills action with instanton gauge fixing. We findN=2 super Yang-Mills theory with Dirac-K{\"a}hler fermions which are generatedfrom ghosts via twisting mechanism. The Weinberg-Salam model is formulated bythe generalized Yang-Mills action which includes Connes's non-commutativegeometry formulation as a particular case. In the end a possible scenario torealize the program is proposed. The formulations given here are by farincomplete towards the final goal yet include hopeful evidences. This summaryof the overview is the extended version of the talk given at Nishinomiya-Yukawamemorial symposium (Nishinomiya-city Japan, Nov. 1998).Comment: LaTeX, 70 pages, 26 eps figure