Supergravities and Branes from Hilbert-Poincar\'e Series

TL;DR

This paper demonstrates how Hilbert-Poincaré series and Molien-Weyl integrals can be used to construct supergravity spectra and nonperturbative objects by computing invariants and cohomology structures.

Contribution

It introduces a novel application of mathematical tools to derive supergravity spectra and nonperturbative objects from gauge invariants.

Findings

Hilbert-Poincaré series can compute invariants for supergravity fields

Method reproduces pure supergravity spectrum

Enables construction of nonperturbative objects

Abstract

The Molien-Weyl integral formula and the Hilbert-Poincar\'e series have proven to be powerful mathematical tools in relation to gauge theories, allowing to count the number of gauge invariant operators. In this paper, we show that these methods can also be employed to construct Free Differential Algebras and, therefore, reproduce the associated pure supergravity spectrum and nonperturbative objects. Indeed, given a set of fields, the Hilbert-Poincar\'e series allows to compute all possible invariants and consequently derive the cohomology structure.