Deformations of Chiral Two-Forms in Six Dimensions

TL;DR

This paper investigates potential local deformations of chiral two-forms in six dimensions, concluding that no suitable local field theory can describe M5-branes due to the limitations found.

Contribution

It provides an exhaustive classification of all possible local deformations of chiral two-forms in six dimensions using BRST cohomology, showing the impossibility of a local field theory for M5-branes.

Findings

No acceptable local deformations exist for chiral two-forms in six dimensions.

The study rules out local field theories for describing M5-branes.

All possible deformations are classified and found insufficient for a consistent M5-brane theory.

Abstract

Motivated by a system consisting of a number of parallel M5-branes, we study possible local deformations of a chiral two-form in six dimensions. Working to first order in the coupling constant, this reduces to the study of the local BRST cohomological group at ghost number zero. We obtain an exhaustive list of all possible deformations. None of them allows for a satisfactory formulation of the M5-branes system leading to the conclusion that no local field theory can describe such a system.