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TMF, 2015 Volume 182, Number 1, Pages 28–64 (Mi tmf8709)

This article is cited in 68 papers

The exact spectrum and mirror duality of the $(\text{AdS}_5{\times}S^5)_\eta$ superstring

G. E. Arutyunovabcd, M. de Leeuwe, S. J. van Tongerenfg

a Steklov Mathematical Institute, Moscow, Russia
b Institute for Theoretical Physics, Utrecht University, Utrecht, The Netherlands
c Spinoza Institute, Utrecht University, Utrecht, The Netherlands
d Institute for Theoretical Physics, Hamburg University, Hamburg, Germany
e ETH Zürich, Institut für Theoretische Physik, Zurich, Switzerland
f Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany
g Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany

Abstract: 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, exact $S$-matrix, thermodynamic Bethe ansatz.

Received: 14.05.2014

DOI: 10.4213/tmf8709


 English version:
Theoretical and Mathematical Physics, 2015, 182:1, 23–51

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