A No-Go Theorem for M5-brane Theory

TL;DR

This paper proves a no-go theorem demonstrating the impossibility of deforming Nambu-Poisson gauge symmetry to fully match noncommutative gauge symmetry in M5-brane theories, highlighting fundamental limitations in their theoretical connection.

Contribution

It establishes a no-go theorem showing that Nambu-Poisson gauge symmetry cannot be deformed to match noncommutative gauge symmetry in 4+1 dimensions, regardless of reduction methods.

Findings

No deformation of Nambu-Poisson gauge symmetry can reproduce full noncommutative gauge symmetry.

The result holds to all orders in perturbation, without assuming a deformation of the Nambu-Poisson bracket.

This imposes fundamental constraints on the theoretical modeling of M5-branes in background fields.

Abstract

The BLG model for multiple M2-branes motivates an M5-brane theory with a novel gauge symmetry defined by the Nambu-Poisson structure. This Nambu-Poisson gauge symmetry for an M5-brane in large C-field background can be matched, on double dimension reduction, with the Poisson limit of the noncommutative gauge symmetry for a D4-brane in B-field background. Naively, one expects that there should exist a certain deformation of the Nambu-Poisson structure to match with the full noncommutative gauge symmetry including higher order terms. However, We prove the no-go theorem that there is no way to deform the Nambu-Poisson gauge symmetry, even without assuming the existence of a deformation of Nambu-Poisson bracket, to match with the noncommutative gauge symmetry in 4+1 dimensions to all order, regardless of how the double dimension reduction is implemented.