[Paper Review] Interactions of chiral two-forms

Xavier Bekaert|ArXiv.org|Nov 15, 1999

Molecular spectroscopy and chirality4 references3 citations

TL;DR

This paper investigates the consistent interactions of chiral two-forms in six-dimensional spacetime, focusing on Lorentz-invariant self-couplings and local deformations. Using the Dirac-Schwinger condition on energy-momentum commutators, it derives the Perry-Schwarz condition and proves that the only consistent local deformations of free chiral two-forms preserve their abelian gauge symmetries, with implications for M5-brane systems.

ABSTRACT

Two issues regarding the interactions of the chiral two-forms are reviewed. First, the problem of constructing Lorentz-invariant self-couplings of a single chiral two-form is investigated in the light of the Dirac-Schwinger condition on the energy-momentum tensor commutation relations. We show how the Perry-Schwarz condition follows from the Dirac-Schwinger criterion and point out that consistency of the gravitational coupling is automatic. Secondly, we study the possible local deformations of chiral two-forms. This problem reduces to the study of the local BRST cohomological group at ghost number zero. We proof that the only consistent deformations of a system of free chiral two-forms are (up to redefinitions) deformations that do not modify the abelian gauge symmetries of the free theory. The consequence of this result for a system consisting of a number of parallel M5-branes is explained.

Motivation & Objective

• To resolve the challenge of constructing Lorentz-invariant self-couplings for a single chiral two-form.
• To examine the consistency of gravitational coupling in the context of chiral two-forms.
• To classify all possible local deformations of free chiral two-form systems.
• To determine the implications of the classification for systems of parallel M5-branes.
• To establish the role of the Dirac-Schwinger condition in deriving the Perry-Schwarz condition for consistency.

Proposed method

• Applies the Dirac-Schwinger criterion on energy-momentum tensor commutation relations to constrain self-couplings.
• Derives the Perry-Schwarz condition as a consequence of the Dirac-Schwinger criterion.
• Uses BRST cohomology at ghost number zero to classify local deformations of chiral two-form theories.
• Analyzes the structure of gauge symmetries under deformation, focusing on preservation of abelian nature.
• Considers the implications of the cohomological classification for M-theory compactifications involving M5-branes.
• Employs a systematic approach to deformations that respects gauge invariance and Lorentz covariance.

Experimental results

Research questions

• RQ1 What conditions ensure Lorentz-invariant self-couplings of a chiral two-form?
• RQ2 How does the Dirac-Schwinger condition lead to the Perry-Schwarz condition in chiral two-form theories?
• RQ3 Can non-abelian deformations be consistently introduced in free chiral two-form systems?
• RQ4 What is the role of gravitational coupling in the consistency of chiral two-form interactions?
• RQ5 What are the complete set of consistent local deformations of free chiral two-forms, up to redefinitions?

Key findings

• The Perry-Schwarz condition emerges naturally as a consequence of the Dirac-Schwinger criterion on energy-momentum commutators.
• Consistency of gravitational coupling for chiral two-forms is automatically satisfied under the derived conditions.
• The only consistent local deformations of free chiral two-forms are those that preserve the abelian gauge symmetry of the original theory.
• All such deformations are equivalent to redefinitions of the fields, meaning no new non-abelian structures can be consistently introduced.
• For a system of multiple parallel M5-branes, the result implies that the effective theory remains abelian in its gauge structure under consistent interactions.
• The BRST cohomological analysis at ghost number zero confirms that no non-trivial consistent deformations exist beyond those preserving abelian gauge symmetry.