Holographic partition function of democratic M-theory

TL;DR

The paper tackles the quantum definition of the partition function for democratic M-theory, where electric and magnetic 4- and 7-form fields are treated on equal footing with Chern–Simons-type couplings. It develops a holographic 12d/11d framework, introduces a non-linear differential cocycle for the $(C_4,C_7)$ system, and defines background couplings that yield Ward identities showing the partition function is a holomorphic section of a line bundle, not a scalar. By enforcing a dual quantum constraint $ig angle F_7+i*F_4ig angle=0$ and fixing consistency constants, it provides explicit conditions under which the full deformed partition function is well-defined and quantized, including an explicit path-integral expression. The work broadens the quantum understanding of higher-form gauge symmetries in M-theory and offers a template for applying democratic formulations to other higher-form theories and charged objects.

Abstract

We study the partition function associated with the democratic formulation of M-theory, focusing on its global definition and quantization properties. Using a path integral representation that makes manifest the underlying cohomological structure, we analyze the coupled system of form fields $C_4$ and $C_7$ and its associated gauge transformations. We show that the resulting description is naturally captured by a non-linear differential cocycle, 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 gauge symmetry, and allows for a consistent definition of the partition function in terms of higher-dimensional auxiliary manifolds.