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arXiv · 1701.06894

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

Hirotaka Sugawara
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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.

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Hirotaka Sugawara. 2017-01-18. Current Algebra Formulation of M-theory based on E11 Kac-Moody Algebra. https://doi.org/10.1142/s0217751x17500245

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