On the Yangian [Y(e8)] quantum symmetry of maximal supergravity in two 
dimensions

Koepsell, Kilian; Nicolai, Hermann; Samtleben, Henning

doi:10.1088/1126-6708/1999/04/023

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On the Yangian [Y(e8)] quantum symmetry of maximal supergravity in two dimensions

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Koepsell, Kilian
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Nicolai, Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Koepsell, K., Nicolai, H., & Samtleben, H. (1999). On the Yangian [Y(e8)] quantum symmetry of maximal supergravity in two dimensions. Journal of High Energy Physics, 1999(4): 023. doi:10.1088/1126-6708/1999/04/023.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-58BD-4

Abstract

We present the algebraic framework for the quantization of the classical bosonic charge algebra of maximally extended (N = 16) supergravity in two dimensions, thereby taking the first steps towards an exact quantization of this model. At the core of our construction is the Yangian algebra Y(fraktur e8) whose RTT presentation we discuss in detail. The full symmetry algebra is a centrally extended twisted version of the Yangian double Script DY(fraktur e8)c. We show that there exists only one special value of the central charge for which the quantum algebra admits an ideal by which the algebra can be divided so as to consistently reproduce the classical coset structure E8(8)/SO in the limit hbar→0.