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arXiv · hep-th/0602007

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

S. Bellucci·P. -Y. Casteill
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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 $S^1_{ϕ_1}\times S^1_{ϕ_1}\times S^1_{ϕ_2}$ in $\rm{AdS}_5 \times S^5$. The full sigma model on the supercoset $SU(1,1|2)/SU(1|1)^2$ is given.

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S. Bellucci, P. -Y. Casteill. 2006-02-13. Sigma model from SU(1,1|2) spin chain. https://doi.org/10.1016/j.nuclphysb.2006.02.021

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