Hodge Duality and Cosmological Constant

TL;DR

This paper introduces a novel mechanism using Hodge duality and Chern-Simons terms to eliminate cosmological constants in various theories, compatible with supersymmetry and applicable to supergravity models.

Contribution

It proposes a new approach leveraging Hodge duality and Chern-Simons terms to address the cosmological constant problem across different theories, including supersymmetric and non-supersymmetric models.

Findings

Successfully applied to four-dimensional N=1 supergravity.

Extended to ten-dimensional type IIA supergravity.

Indicates potential for quantum system applications.

Abstract

We present a simple mechanism to eliminate cosmological constants both in supersymmetric and non-supersymmetric theories. This mechanism is based on the Hodge (Poincare) duality between a 0-form and D-form field strengths in D-dimensional space-time. The new key ingredient is the introduction of an extra Chern-Simons term into the D-form field strength H dual to the 0-form field strength. Our formulation can be also made consistent with supersymmetry. Typical applications to four-dimensional N=1 supergravity and to ten-dimensional type IIA supergravity are given. The success of our formulation for both supersymmetric and non-supersymmetric systems strongly indicates the validity of our mechanism even after supersymmetry breakings at the classical level. Our mechanism may well be applicable to quantized systems, at least for supersymmetric cases with fundamental D-brane actions available.