A brief review of E theory

Abstract

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of non-linear realisations and Kac-Moody algebras, I explain how to construct the non-linear realisation based on the Kac-Moody algebra E11 and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space time, lead to precisely the equations of motion of eleven dimensional supergravity theory. By taking different group decompositions of E11 we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the non-linear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the E11 conjecture given many years ago.

arXiv commentTo appear in the Proceedings of Abdus Salam's 90th Birthday meeting, 25-28 January 2016, NTU, Singapore, Editors L. Brink, M. Duff and K. Phua, World Scientific Publishing

References in corpus (35)

• Unity of Superstring Dualities
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• E_11 and M Theory
• An Sl(2,Z) Multiplet of Nine-Dimensional Type II Supergravity Theories
• $E_{11}$, SL(32) and Central Charges
• Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems
• The E_{11} origin of all maximal supergravities
• The maximal D=5 supergravities
• Very-extended Kac-Moody algebras and their interpretation at low levels
• E(11) and the Embedding Tensor
• Hidden Superconformal Symmetry in M Theory
• Very Extended $E_8$ and $A_8$ at low levels, Gravity and Supergravity
• The IIA, IIB and eleven dimensional theories and their common E_{11} origin
• Kac-Moody Symmetries of IIB Supergravity
• G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions
• Frame-like Geometry of Double Field Theory
• IIB Supergravity Revisited
• Representations of G+++ and the role of space-time
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• E(11)-extended spacetime and gauged supergravities
• IIA Ten-forms and the Gauge Algebras of Maximal Supergravity Theories
• E11, generalised space-time and IIA string theory
• E11 in 11D
• Brane dynamics, central charges and E_{11}
• Generalised geometry, eleven dimensions and E11
• Charge multiplets and masses for E(11)
• The E(11) origin of all maximal supergravities - the hierarchy of field-strengths
• E11, generalised space-time and IIA string theory; the R-R sector
• E11, generalised space-time and equations of motion in four dimensions
• E11 must be a symmetry of strings and branes
• E_{11}, ten forms and supergravity
• E_{11} and Higher Spin Theories
• Duality Symmetries and G^{+++} Theories
• E11 and Supersymmetry
• Generalised vielbeins and non-linear realisations

Cited by in corpus (19)

• The Odd story of ${\alpha }^{\prime }$-corrections
• E11, Romans theory and higher level duality relations
• Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras
• The non-linear dual gravity equation of motion in eleven dimensions
• On the different formulations of the E11 equations of motion
• Partition function of Chern-Simons theory as renormalized q-dimension
• Irreducible representations of E theory
• Massive Dual Gravity in N Spacetime Dimensions
• D = 3 Unification of Curious Supergravities
• Gravity, Dual Gravity and A1+++
• An E11 invariant gauge fixing
• Spacetime and large local transformations
• Higher dualisations of linearised gravity and the $A_1^{+++}$ algebra
• $\mathcal{S}$-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions
• E theory in seven dimensions
• Unfolding $E_{11}$
• M2- and M5-branes in E11 Current Algebra Formulation of M-theory
• Current Algebra Formulation of Quantum Gravity and Its Application to Cosmology
• Kac-Moody algebras and the cosmological constant