The full Quantum Spectral Curve for $AdS_4/CFT_3$

Diego Bombardelli; Andrea Cavaglià; Davide Fioravanti; Nikolay Gromov; Roberto Tateo

doi:10.1007/JHEP09(2017)140

The full Quantum Spectral Curve for $AdS_4/CFT_3$

Diego Bombardelli, Andrea Cavaglià, Davide Fioravanti, Nikolay Gromov, Roberto Tateo

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Abstract

The spectrum of planar N=6 superconformal Chern-Simons theory, dual to type IIA superstring theory on $AdS_4 \times CP^3$, is accessible at finite coupling using integrability. Starting from the results of [arXiv:1403.1859], we study in depth the basic integrability structure underlying the spectral problem, the Quantum Spectral Curve. The new results presented in this paper open the way to the quantitative study of the spectrum for arbitrary operators at finite coupling. Besides, we show that the Quantum Spectral Curve is embedded into a novel kind of Q-system, which reflects the OSp(4|6) symmetry of the theory and leads to exact Bethe Ansatz equations. The discovery of this algebraic structure, more intricate than the one appearing in the $AdS_5/CFT_4$ case, could be a first step towards the extension of the method to $AdS_3/CFT_2$.

Original language	English
Number of pages	65
Journal	JHEP
Early online date	27 Sept 2017
DOIs	https://doi.org/10.1007/JHEP09(2017)140
Publication status	E-pub ahead of print - 27 Sept 2017

Keywords

hep-th

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10.1007/JHEP09(2017)140Licence: CC BY

The full Quantum Spectral_BOMBARDELLI_Accepted24August2017_GOLD VoR (CC BY)Final published version, 1.02 MBLicence: CC BY

Cite this

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title = "The full Quantum Spectral Curve for $AdS_4/CFT_3$",

abstract = "The spectrum of planar N=6 superconformal Chern-Simons theory, dual to type IIA superstring theory on $AdS_4 \times CP^3$, is accessible at finite coupling using integrability. Starting from the results of [arXiv:1403.1859], we study in depth the basic integrability structure underlying the spectral problem, the Quantum Spectral Curve. The new results presented in this paper open the way to the quantitative study of the spectrum for arbitrary operators at finite coupling. Besides, we show that the Quantum Spectral Curve is embedded into a novel kind of Q-system, which reflects the OSp(4|6) symmetry of the theory and leads to exact Bethe Ansatz equations. The discovery of this algebraic structure, more intricate than the one appearing in the $AdS_5/CFT_4$ case, could be a first step towards the extension of the method to $AdS_3/CFT_2$.",

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author = "Diego Bombardelli and Andrea Cavagli{\`a} and Davide Fioravanti and Nikolay Gromov and Roberto Tateo",

note = "41 pages + 5 Appendices, 7 figures. v3: text improved, typos fixed, references added, more details in Appendix A",

year = "2017",

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T1 - The full Quantum Spectral Curve for $AdS_4/CFT_3$

AU - Bombardelli, Diego

AU - Cavaglià, Andrea

AU - Fioravanti, Davide

AU - Gromov, Nikolay

AU - Tateo, Roberto

N1 - 41 pages + 5 Appendices, 7 figures. v3: text improved, typos fixed, references added, more details in Appendix A

PY - 2017/9/27

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N2 - The spectrum of planar N=6 superconformal Chern-Simons theory, dual to type IIA superstring theory on $AdS_4 \times CP^3$, is accessible at finite coupling using integrability. Starting from the results of [arXiv:1403.1859], we study in depth the basic integrability structure underlying the spectral problem, the Quantum Spectral Curve. The new results presented in this paper open the way to the quantitative study of the spectrum for arbitrary operators at finite coupling. Besides, we show that the Quantum Spectral Curve is embedded into a novel kind of Q-system, which reflects the OSp(4|6) symmetry of the theory and leads to exact Bethe Ansatz equations. The discovery of this algebraic structure, more intricate than the one appearing in the $AdS_5/CFT_4$ case, could be a first step towards the extension of the method to $AdS_3/CFT_2$.

AB - The spectrum of planar N=6 superconformal Chern-Simons theory, dual to type IIA superstring theory on $AdS_4 \times CP^3$, is accessible at finite coupling using integrability. Starting from the results of [arXiv:1403.1859], we study in depth the basic integrability structure underlying the spectral problem, the Quantum Spectral Curve. The new results presented in this paper open the way to the quantitative study of the spectrum for arbitrary operators at finite coupling. Besides, we show that the Quantum Spectral Curve is embedded into a novel kind of Q-system, which reflects the OSp(4|6) symmetry of the theory and leads to exact Bethe Ansatz equations. The discovery of this algebraic structure, more intricate than the one appearing in the $AdS_5/CFT_4$ case, could be a first step towards the extension of the method to $AdS_3/CFT_2$.

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