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arXiv · 0704.1460

Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence

B. Stefanski Jr
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Abstract

We define Landau-Lifshitz sigma models on general coset space $G/H$, with $H$ a maximal stability sub-group of $G$. These are non-relativistic models that have $G$-valued Nöther charges, local $H$ invariance and are classically integrable. Using this definition, we construct the $PSU(2,2|4)/PS(U(2|2)^2)$ Landau-Lifshitz sigma-model. This sigma model describes the thermodynamic limit of the spin-chain Hamiltonian obtained from the complete one-loop dilatation operator of the N=4 super Yang-Mills (SYM) theory. In the second part of the paper, we identify a number of consistent truncations of the Type IIB Green-Schwarz action on $AdS_5\times S^5$ whose field content consists of two real bosons and 4,8 or 16 real fermions. We show that $κ$-symmetry acts trivially in these sub-sectors. In the context of the large spin limit of the AdS/CFT correspondence, we map the Lagrangians of these sub-sectors to corresponding truncations of the $PSU(2,2|4)/PS(U(2|2)^2)$ Landau-Lifshitz sigma-model.

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B. Stefanski Jr. 2007-04-11. Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence. https://doi.org/10.1088/1126-6708%2F2007%2F07%2F009

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