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

Stefanski, B. (2007). Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence. Journal of High Energy Physics, 2007(7), doi: 10.1088/1126-6708/2007/07/009

## 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 N\"other 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 $\kappa$-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.

Publication Type: Article Q Science > QC Physics School of Mathematics, Computer Science & Engineering > Mathematics Author http://openaccess.city.ac.uk/id/eprint/1021
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