Conformal Non-Geometric Gravity in Six Dimensions and M-Theory above the Planck Energy

TL;DR

This paper explores a six-dimensional superconformal phase of M-theory emerging at strong coupling, characterized by a (4,0) supersymmetric tensor gauge field, and discusses its potential for a new geometric understanding of gravity.

Contribution

It introduces a free 6D (4,0) superconformal theory with a tensor gauge field, proposing a novel phase of M-theory beyond the Planck scale.

Findings

The free 6D theory has a Riemann-like tensor gauge field.

Dimensional reduction yields linearized 5D gravity.

Discussion on possible interactions and geometric implications.

Abstract

The proposal that a strong coupling limit of the five-dimensional type II string theory (M-theory compactified on a 6-torus) in which the Planck length becomes infinite could give a six-dimensional superconformal phase of M-theory is reviewed. This limit exists for the free theory, giving a 6-dimensional theory with (4,0) supersymmetry compactified on a circle whose radius gives the 5-dimensional Planck length. The free 6-dimensional theory has a fourth rank tensor gauge field with the symmetries of the Riemann tensor instead of a symmetric tensor gauge field, but its dimensional reduction gives conventional linearised gravity in five dimensions. The possibility of an interacting form of this theory existing and the consequences it would have for the geometric picture of gravity are discussed.