Z Theory

TL;DR

This work proposes $Z$-theory as a topological analogue of M-theory, unifying the corners of topological strings—Gromov–Witten, Donaldson–Thomas, Kodaira–Spencer, and Donaldson–Witten—through a common partition function and higher-dimensional perspectives. It builds evidence via A/B-model stories, nonperturbative D-brane corrections, and a DW/gauge-theory framework, and introduces seven-dimensional Hitchin-type formalisms (H6/H7) for a unified description of complex and Kähler moduli. The author then outlines a path toward unification using spinor Chern–Simons-like actions, spectral-action ideas, and possible eight-dimensional extensions, suggesting a deeper nonperturbative topological gravity theory. If realized, this framework could provide a coherent, higher-dimensional description of topological string theory and its nonperturbative data, intimately tying D-branes, associative cycles, and flux compactifications into a single geometric-quantum structure.

Abstract

We present the evidence for the existence of the topological string analogue of M-theory, which we call Z-theory. The corners of Z-theory moduli space correspond to the Donaldson-Thomas theory, Kodaira-Spencer theory, Gromov-Witten theory, and Donaldson-Witten theory. We discuss the relations of Z-theory with Hitchin's gravities in six and seven dimensions, and make our own proposal, involving spinor generalization of Chern-Simons theory of three-forms. Based on the talk at Strings'04 in Paris.