Lie algebra expansion and integrability in superstring sigma-models

DOI10.1007/JHEP07(2020)083zbMATH Open1451.83093arXiv2005.01736WikidataQ115390682 ScholiaQ115390682MaRDI QIDQ2215375

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Publication date: 11 December 2020

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Abstract: Lie algebra expansion is a technique to generate new Lie algebras from a given one. In this paper, we apply the method of Lie algebra expansion to superstring $sigma$-models with a $mathbb{Z}_4$ coset target space. By applying the Lie algebra expansion to the isometry algebra, we obtain different $sigma$-models, where the number of dynamical fields can change. We reproduce and extend in a systematic way actions of some known string regimes (flat space, BMN and non-relativistic in AdS${}_{5}imes$S${}^5$). We define a criterion for the algebra truncation such that the equations of motion of the expanded action of the new $sigma$-model are equivalent to the vanishing curvature condition of the Lax connection obtained by expanding the Lax connection of the initial model.

Full work available at URL: https://arxiv.org/abs/2005.01736

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