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

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 $Ad{S}_5\times S^5$ 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.

42 pages

References in corpus (5)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• On AdS_5 x S^5 String S-matrix
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• On the Hopf algebra structure of the AdS/CFT S-matrix

Cited by in corpus (10)

• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• Superuniversality of superdiffusion
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings
• Structure of the string R-matrix
• Chaotic spin chains in AdS/CFT
• Spin chain from membrane and the Neumann-Rosochatius integrable system
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• The $\mathrm{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten spin-chain $\sigma$-model
• An integrable deformed Landau-Lifshitz model with particle production?