Sigma model from SU(1,1|2) spin chain

Abstract

We derive the coherent state representation of the integrable spin chain Hamiltonian with supersymmetry group $SU(1,1|2)$. By the use of a projected Hamiltonian onto bosonic states, we give explicitly the action of the Hamiltonian on $SU(2)\times SL(2)$ coherent states. Passing to the continuous limit, we find that the corresponding bosonic sigma model is the sum of the known SU(2) and SL(2) ones, and thus it gives a string spinning fast on $S_{{\varphi }_1}^1\times S_{{\varphi }_1}^1\times S_{{\varphi }_2}^1$ in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$. The full sigma model on the supercoset $SU(1,1|2)/SU(1|1{)}^2$ is given.

20 pages, no figures, 4 tables, 1 appendix; typos corrected, references added

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• Aspects of Nonrelativistic Strings
• Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT
• Aspects of Non-Relativistic Quantum Field Theories
• Reconstructing 1/2 BPS Space-Time Metrics from Matrix Models and Spin Chains
• The Panorama of Spin Matrix Theory
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• On S-Matrix factorization of the Landau-Lifshitz model
• The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry
• 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
• The $SU(2)$ Wess-Zumino-Witten spin chain sigma model
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• An integrable deformed Landau-Lifshitz model with particle production?
• The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5