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The exact spectrum and mirror duality of the \((\mathrm{AdS}_5\times S^5)_\eta\) superstring. (English. Russian original) Zbl 1317.81211

Theor. Math. Phys. 182, No. 1, 23-51 (2015); translation from Teor. Mat. Fiz. 182, No. 1, 28-64 (2015).
Summary: We discuss the spectrum of a string propagating on \(\eta\)-deformed \(\mathrm{AdS}_5\times S^5\) by treating its worldsheet theory as an integrable quantum field theory. The exact S-matrix of this field theory is given by a qdeformation of the \(\mathrm{AdS}_5\times S^5\) 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.

MSC:

81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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