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

References in corpus (3)

• Spinning strings and AdS/CFT duality
• Chaining spins from (super)Yang--Mills
• Non-planar spin bits beyond two loops

Cited by in corpus (2)

• Reconstructing 1/2 BPS Space-Time Metrics from Matrix Models and Spin Chains
• The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry