
J. Phys. A, 2014, Volume 47, Issue 8, 85401, 20 pages
(Mi jpha13)




Static gauge and energy spectrum of singlemode strings in $\mathrm{AdS_5\times S^5}$
S. Frolov^{abc}, M. Heinze^{d}, G. Jorjadze^{def}, J. Plefka^{d} ^{a} Hamilton Mathematics Institute and School of Mathematics, Trinity College, Dublin 2, Ireland
^{b} Steklov Mathematical Institute, Moscow
^{c} Institut für Mathematik und Institut für Physik, HumboldtUniversität zu Berlin, IRIS Adlershof, Zum Großen Windkanal 6, D12489 Berlin, Germany
^{d} Institut für Physik, HumboldtUniversität zu Berlin, Newtonstraße 15, D12489 Berlin, Germany
^{e} Razmadze Mathematical Institute of JSU , Tbilisi, Georgia
^{f} FU of Tbilisi, University Campus, David Aghmashenebeli Alley, Tbilisi, Georgia
Abstract:
Motivated by the notorious difficulties in determining the first quantum corrections to the spectrum of short strings in $\mathrm{AdS_5\times S^5}$ from first principles, we study closed bosonic strings in this background employing a static gauge. In this gauge the worldsheet Hamiltonian density is constant along the extension of the string and directly proportional to the square of the spacetime energy. We quantize this system in a minisuperspace approach, in which we consider only a single $\mathrm{AdS_5}$ stringmode excitation next to an arbitrary particle like zeromode contribution in the full $\mathrm{AdS_5\times S^5}$ background. We determine the quantum spectrum using this method to the nexttonexttoleading order in the large 't Hooft coupling expansion. We argue for an ordering prescription which should arise from supersymmetrization and indeed recover the integrability based predictions for the spectrum of the lightest excitation, dual to the Konishi field scaling dimensions. The higher excitations fail to agree, but this is shown to be a consequence of the stringmode truncation employed. Despite this simple setup, our system reveals intriguing features, such as a close connection to particles in $\mathrm{AdS_6}$, classical integrability and preservation of the isometries of $\mathrm{AdS_5\times S^5}$ at the quantum level.
Funding Agency 
Grant Number 
Volkswagen Foundation 

European Union's Seventh Framework Programme 
317089 
Deutsche Forschungsgemeinschaft 
SFB 647 
Science Foundation Ireland 
09/RFP/PHY2142 
The research leading to these results has received funding from the VolkswagenFoundation, the International Max Planck Research School for Geometric Analysis, Gravitation and String Theory, and the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/20072013/ under REA grant agreement no 317089. SF is supported by a DFG grant in the framework of the SFB 647 RaumZeitMaterie. Analytische und Geometrische Strukturen and by the Science Foundation Ireland under grant 09/RFP/PHY2142. 
DOI:
https://doi.org/10.1088/17518113/47/8/085401
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Received: 15.11.2013 Accepted:23.12.2013
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