Non-String Pursuit towards Unified Model on the Lattice

TL;DR

This paper explores a generalized gauge theory framework on the lattice aiming for a unified model, proposing a lattice Chern-Simons gravity theory and connecting to various advanced theories like super Yang-Mills and the Weinberg-Salam model.

Contribution

It introduces a novel lattice formulation based on differential forms and generalized gauge theories, linking discrete models to continuum theories including gravity and particle physics.

Findings

Proposes a lattice Chern-Simons gravity theory leading to continuum limit.

Identifies N=2 super Yang-Mills with Dirac-Kähler fermions from ghost fields.

Formulates the Weinberg-Salam model within the generalized gauge theory framework.

Abstract

Non-standard overview on the possible formulation towards a unified model on the lattice is presented. It is based on the generalized gauge theory which is formulated by differential forms and thus expected to fit in a simplicial manifold. We first review suggestive known results towards this direction. As a small step of concrete realization of the program, we propose a lattice Chern-Simons gravity theory which leads to the Chern-Simons gravity in the continuum limit via Ponzano-Regge model. We then summarize the quantization procedure of the generalized gauge theory and apply the formulation to the generalized topological Yang-Mills action with instanton gauge fixing. We find N=2 super Yang-Mills theory with Dirac-K{\"a}hler fermions which are generated from ghosts via twisting mechanism. The Weinberg-Salam model is formulated by the generalized Yang-Mills action which includes Connes's non-commutative geometry formulation as a particular case. In the end a possible scenario to realize the program is proposed. The formulations given here are by far incomplete towards the final goal yet include hopeful evidences. This summary of the overview is the extended version of the talk given at Nishinomiya-Yukawa memorial symposium (Nishinomiya-city Japan, Nov. 1998).