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

This article is cited in 50 scientific papers (total in 50 papers)

The exact spectrum and mirror duality of the $(AdS_5{\times}S^5)_\eta$ 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

Funding Agency Grant Number
Einstein Stiftung Berlin
European Union's Seventh Framework Programme 317089
Netherlands Organization for Scientific Research VICI 680-47-602
European Research Council 246974
Swiss National Science Foundation 200021-137616
This work is supported in part (S. J. van T.) by the Einstein Foundation Berlin (in the framework of the research project ‘`Gravitation and High Energy Physics") and the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ (REA Grant Agreement No. 317089), in part (G. E. A.) by the Netherlands Organization for Scientific Research (NWO) (VICI Grant No. 680-47-602), the ERC (Advanced grant research program No. 246974, "Supersymmetry: a window to non-perturbative physics"), and the D-ITP consortium, a program of the NWO funded by the Dutch Ministry of Education, Culture and Science (OCW), and in part (M. de L.) by the Swiss National Science Foundation (Grant No. 200021-137616).


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

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Received: 14.05.2014

Citation: G. E. Arutyunov, M. de Leeuw, S. J. van Tongeren, “The exact spectrum and mirror duality of the $(AdS_5{\times}S^5)_\eta$ superstring”, TMF, 182:1 (2015), 28–64; Theoret. and Math. Phys., 182:1 (2015), 23–51

Citation in format AMSBIB
\Bibitem{AruDe Van15}
\by G.~E.~Arutyunov, M.~de Leeuw, S.~J.~van Tongeren
\paper The~exact spectrum and mirror duality of the~$(\text{AdS}_5{\times}S^5)_\eta$ superstring
\jour TMF
\yr 2015
\vol 182
\issue 1
\pages 28--64
\jour Theoret. and Math. Phys.
\yr 2015
\vol 182
\issue 1
\pages 23--51

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