# Current Algebra Formulation of M-theory based on E11 Kac-Moody Algebra

## TL;DR

This paper develops a quantum M-theory framework using E11 Kac-Moody algebra, unifying internal gauge and gravity theories through current algebra, and introduces a novel quantum gravity equation differing from Einstein-Hilbert predictions.

## Contribution

It introduces a current algebra formulation of M-theory based on E11, integrating supersymmetry and deriving quantum equations of motion for gravity and gauge fields.

## Key findings

- Unified internal gauge and gravity theories within E11 algebra
- Quantum gravity equation differs from Einstein-Hilbert formulation
- Supersymmetry incorporated naturally via current algebra

## Abstract

Quantum M-theory is formulated using the current algebra technique. The current algebra is based on a Kac-Moody algebra rather than usual finite dimensional Lie algebra. Specifically, I study the $E_{11}$ Kac-Moody algebra that was shown recently to contain all the ingredients of M-theory. Both the internal symmetry and the external Lorentz symmetry can be realized inside $E_{11}$, so that, by constructing the current algebra of $E_{11}$, I obtain both internal gauge theory and gravity theory. The energy-momentum tensor is constructed as the bilinear form of the currents, yielding a system of quantum equations of motion of the currents/fields. Supersymmetry is incorporated in a natural way. The so-called "field-current identity" is built in and, for example, the gravitino field is itself a conserved super-current. One unanticipated outcome is that the quantum gravity equation is not identical to the one obtained from the Einstein-Hilbert action.