Geodesic
The~exact spectrum and mirror duality of the~$(\text{AdS}_5{\times}S^5)_\eta$ superstring
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 28-64

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We discuss the spectrum of a string propagating on $\eta$-deformed AdS$_5\times S^5$ by treating its worldsheet theory as an integrable quantum field theory. The exact $S$-matrix of this field theory is given by a $q$-deformation of the AdS$_5{\times}S^5$ worldsheet $S$-matrix with a real deformation parameter. By considering mirror (double Wick-rotated) versions of these worldsheet theories, we give the thermodynamic Bethe ansatz description of their exact finite-size spectra. Interestingly, this class of models maps onto itself under the mirror transformation. At the string level, this seems to indicate that the light-cone worldsheet theories of strings on particular pairs of backgrounds are related by a double Wick rotation, a feature we call “mirror duality”. We provide a partial verification of these statements at the level of a sigma model by considering reduced actions and their corresponding (mirror) giant magnon solutions.
Keywords: AdS/CFT correspondence, sigma model, thermodynamic Bethe ansatz.
Mots-clés : exact $S$-matrix 
@article{TMF_2015_182_1_a1,
     author = {G. E. Arutyunov and M. de Leeuw and S. J. van Tongeren},
     title = {The~exact spectrum and mirror duality of the~$(\text{AdS}_5{\times}S^5)_\eta$ superstring},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {28--64},
     publisher = {mathdoc},
     volume = {182},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a1/}
}
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G. E. Arutyunov; M. de Leeuw; S. J. van Tongeren. The~exact spectrum and mirror duality of the~$(\text{AdS}_5{\times}S^5)_\eta$ superstring. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 28-64. http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a1/