Topological Symmetry of forms, N=1 Supersymmetry and S-duality on Special Manifolds

TL;DR

This paper explores the quantization of holomorphic two-forms on special manifolds, revealing connections to supersymmetric theories, topological quantum field theories, and S-duality, with implications for string theory and M-theory.

Contribution

It introduces a framework linking holomorphic two-form quantization to twisted supersymmetry and topological theories on special manifolds, extending to higher dimensions and dualities.

Findings

Relation between topological models and N=1 Super Yang-Mills

Partition function linked to holomorphic Chern-Simons theory

Potential role of two-form fields in S-duality studies

Abstract

We study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT's (Almost Topological Quantum Field Theories), that is, theories with observables that are invariant under changes of metrics belonging to restricted classes. For Kahler manifolds in four dimensions, our topological model is related to N=1 Super Yang-Mills theory. Extended supersymmetries are recovered by considering the coupling with chiral multiplets. We also analyse Calabi-Yau manifolds in six and eight dimensions, and seven dimensional G_2 manifolds of the kind recently discussed by Hitchin. We argue that the two-form field could play an interesting role for the study of the conjectured S-duality in topological string. We finally show that in the case of real forms in six dimensions the partition function of our topological model is related to the square of that of the holomorphic Chern-Simons theory, and we discuss the uplift to seven dimensions and its relation with the recent proposals for the topological M-theory.