Holographic partition function of democratic M-theory

TL;DR

This paper investigates the global and quantum aspects of the partition function in democratic M-theory, revealing a Heisenberg group structure and clarifying higher-form symmetries through a cohomological path-integral approach.

Contribution

It introduces a cohomological path-integral framework for M-theory's partition function, highlighting a Heisenberg group structure and the role of higher-form symmetries.

Findings

Identifies a Heisenberg-type group structure in M-theory partition function

Provides a global definition of the partition function using auxiliary manifolds

Clarifies the role of higher-form global symmetries in M-theory

Abstract

We study the partition function associated with the democratic formulation of M-theory, focusing on its global definition and quantum properties. Using a path-integral representation that makes manifest the underlying cohomological structure, we analyze the coupled system of M-theory form fields $(A_3 + A_6)$, and the background fields $(C_4 + C_7)$, as well as their associated global transformations. We show that the resulting description is naturally captured by a Heisenberg-type group reflecting the presence of a quadratic coupling between electric and magnetic degrees of freedom. This framework provides a transparent characterization of the global structure of the theory, clarifies the role of higher-form global symmetry, and allows for a consistent definition of the partition function in terms of higher-dimensional auxiliary manifolds.