Abstract
We investigate the solution space of the β-deformed Quantum Spectral Curve by studying a sample of solutions corresponding to single-trace operators that in the undeformed theory belong to the Konishi multiplet. We discuss how to set the precise boundary conditions for the leading Q-system for a given state, how to solve it, and how to build perturbative corrections to the Pμ-system. We confirm and add several loop orders to known results in the literature.
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N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for planar \( \mathcal{N} \) = 4 Super-Yang-Mills theory, Phys. Rev. Lett.112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for arbitrary state/operator in AdS 5/CFT 4 , JHEP09 (2015) 187 [arXiv:1405.4857] [INSPIRE].
N. Gromov, F. Levkovich-Maslyuk, G. Sizov and S. Valatka, Quantum spectral curve at work: from small spin to strong coupling in \( \mathcal{N} \) = 4 SYM, JHEP07 (2014) 156 [arXiv:1402.0871] [INSPIRE].
M. Alfimov, N. Gromov and V. Kazakov, QCD Pomeron from AdS/CFT quantum spectral curve, JHEP07 (2015) 164 [arXiv:1408.2530] [INSPIRE].
C. Marboe and D. Volin, Quantum spectral curve as a tool for a perturbative quantum field theory, Nucl. Phys.B 899 (2015) 810 [arXiv:1411.4758] [INSPIRE].
C. Marboe, V. Velizhanin and D. Volin, Six-loop anomalous dimension of twist-two operators in planar \( \mathcal{N} \) = 4 SYM theory, JHEP07 (2015) 084 [arXiv:1412.4762] [INSPIRE].
N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Quantum spectral curve and the numerical solution of the spectral problem in AdS 5/CFT 4 , JHEP06 (2016) 036 [arXiv:1504.06640] [INSPIRE].
N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Pomeron eigenvalue at three loops in \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett.115 (2015) 251601 [arXiv:1507.04010] [INSPIRE].
A. Hegedűs and J. Konczer, Strong coupling results in the AdS 5/CFT 4correspondence from the numerical solution of the quantum spectral curve, JHEP08 (2016) 061 [arXiv:1604.02346] [INSPIRE].
C. Marboe and V. Velizhanin, Twist-2 at seven loops in planar \( \mathcal{N} \) = 4 SYM theory: full result and analytic properties, JHEP11 (2016) 013 [arXiv:1607.06047] [INSPIRE].
N. Gromov and F. Levkovich-Maslyuk, Quark-anti-quark potential in \( \mathcal{N} \) = 4 SYM, JHEP12 (2016) 122 [arXiv:1601.05679] [INSPIRE].
C. Marboe and D. Volin, The full spectrum of AdS5/CFT4 I: representation theory and one-loop Q-system, J. Phys.A 51 (2018) 165401 [arXiv:1701.03704] [INSPIRE].
C. Marboe and D. Volin, The full spectrum of AdS 5/CFT 4II: weak coupling expansion via the quantum spectral curve, arXiv:1812.09238 [INSPIRE].
M. Alfimov, N. Gromov and G. Sizov, BFKL spectrum of \( \mathcal{N} \) = 4: non-zero conformal spin, JHEP07 (2018) 181 [arXiv:1802.06908] [INSPIRE].
A. Cavaglià, N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve and structure constants in \( \mathcal{N} \) = 4 SYM: cusps in the ladder limit, JHEP10 (2018) 060 [arXiv:1802.04237] [INSPIRE].
T. Harmark and M. Wilhelm, The Hagedorn temperature of AdS 5/CFT 4at finite coupling via the quantum spectral curve, Phys. Lett.B 786 (2018) 53 [arXiv:1803.04416] [INSPIRE].
N. Gromov et al., Integrability of conformal fishnet theory, JHEP01 (2018) 095 [arXiv:1706.04167] [INSPIRE].
A. Cavaglià, D. Fioravanti, N. Gromov and R. Tateo, Quantum spectral curve of the \( \mathcal{N} \) = 6 supersymmetric Chern-Simons theory, Phys. Rev. Lett.113 (2014) 021601 [arXiv:1403.1859] [INSPIRE].
D. Bombardelli et al., The full quantum spectral curve for AdS 4/CFT 3, JHEP09 (2017) 140 [arXiv:1701.00473] [INSPIRE].
N. Gromov and G. Sizov, Exact slope and interpolating functions in N = 6 supersymmetric Chern-Simons theory, Phys. Rev. Lett.113 (2014) 121601 [arXiv:1403.1894] [INSPIRE].
L. Anselmetti, D. Bombardelli, A. Cavaglià and R. Tateo, 12 loops and triple wrapping in ABJM theory from integrability, JHEP10 (2015) 117 [arXiv:1506.09089] [INSPIRE].
A. Cavaglià, N. Gromov and F. Levkovich-Maslyuk, On the exact interpolating function in ABJ theory, JHEP12 (2016) 086 [arXiv:1605.04888] [INSPIRE].
D. Bombardelli, A. Cavaglià, R. Conti and R. Tateo, Exploring the spectrum of planar AdS 4/CFT 3at finite coupling, JHEP04 (2018) 117 [arXiv:1803.04748] [INSPIRE].
R.N. Lee and A.I. Onishchenko, ABJM quantum spectral curve and Mellin transform, JHEP05 (2018) 179 [arXiv:1712.00412] [INSPIRE].
R.N. Lee and A.I. Onishchenko, Toward an analytic perturbative solution for the ABJM quantum spectral curve, arXiv:1807.06267 [INSPIRE].
V. Kazakov, S. Leurent and D. Volin, T-system on T-hook: grassmannian solution and twisted quantum spectral curve, JHEP12 (2016) 044 [arXiv:1510.02100] [INSPIRE].
N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve for a cusped Wilson line in \( \mathcal{N} \) = 4 SYM, JHEP04 (2016) 134 [arXiv:1510.02098] [INSPIRE].
O. Gürdoğan and V. Kazakov, New integrable 4D quantum field theories from strongly deformed planar \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett.117 (2016) 201602 [arXiv:1512.06704] [INSPIRE].
R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys.B 447 (1995) 95 [hep-th/9503121] [INSPIRE].
O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP05 (2005) 033 [hep-th/0502086] [INSPIRE].
R. Roiban, On spin chains and field theories, JHEP09 (2004) 023 [hep-th/0312218] [INSPIRE].
F. Fiamberti, A. Santambrogio, C. Sieg and D. Zanon, Finite-size effects in the superconformal beta-deformed N = 4 SYM, JHEP08 (2008) 057 [arXiv:0806.2103] [INSPIRE].
F. Fiamberti, A. Santambrogio, C. Sieg and D. Zanon, Single impurity operators at critical wrapping order in the beta-deformed N = 4 SYM, JHEP08 (2009) 034 [arXiv:0811.4594] [INSPIRE].
J. Fokken, C. Sieg and M. Wilhelm, The complete one-loop dilatation operator of planar real β-deformed \( \mathcal{N} \) = 4 SYM theory, JHEP07 (2014) 150 [arXiv:1312.2959] [INSPIRE].
M. Wilhelm, Form factors and the dilatation operator in \( \mathcal{N} \) = 4 super Yang-Mills theory and its deformations, Ph.D. thesis, Humboldt University, Berlin, Germany (2016), arXiv:1603.01145 [INSPIRE].
J. Fokken, A hitchhiker’s guide to quantum field theoretic aspects of \( \mathcal{N} \) = 4 SYM theory and its deformations, Ph.D. thesis, Humboldt University, Berlin, Germany (2017), arXiv:1701.00785 [INSPIRE].
G. Arutyunov, M. de Leeuw and S.J. van Tongeren, Twisting the Mirror TBA, JHEP02 (2011) 025 [arXiv:1009.4118] [INSPIRE].
N. Gromov and F. Levkovich-Maslyuk, Y-system and β-deformed N = 4 Super-Yang-Mills, J. Phys.A 44 (2011) 015402 [arXiv:1006.5438] [INSPIRE].
M. de Leeuw and T. Lukowski, Twist operators in N = 4 beta-deformed theory, JHEP04 (2011) 084 [arXiv:1012.3725] [INSPIRE].
M. Beccaria, F. Levkovich-Maslyuk and G. Macorini, On wrapping corrections to GKP-like operators, JHEP03 (2011) 001 [arXiv:1012.2054] [INSPIRE].
C. Ahn, Z. Bajnok, D. Bombardelli and R.I. Nepomechie, Finite-size effect for four-loop Konishi of the β-deformed N = 4 SYM, Phys. Lett.B 693 (2010) 380 [arXiv:1006.2209] [INSPIRE].
M. Günaydin and D. Volin, The complete unitary dual of non-compact Lie superalgebra su(p, q|m) via the generalised oscillator formalism and non-compact Young diagrams, Commun. Math. Phys.367 (2019) 873 [arXiv:1712.01811] [INSPIRE].
C. Marboe, The AdS/CFT spectrum via integrability-based algorithms, Ph.D. thesis, Trinity College, Dublin Ireland (2017).
S. Leurent and D. Volin, Multiple zeta functions and double wrapping in planar \( \mathcal{N} \) = 4 SYM, Nucl. Phys.B 875 (2013) 757 [arXiv:1302.1135] [INSPIRE].
F. Brown, Single-valued motivic periods and multiple Zeta values, SIGMA2 (2014) e25 [arXiv:1309.5309] [INSPIRE].
O. Schnetz, Graphical functions and single-valued multiple polylogarithms, Commun. Num. Theor. Phys.08 (2014) 589 [arXiv:1302.6445] [INSPIRE].
J. Caetano, O. Gürdoğan and V. Kazakov, Chiral limit of \( \mathcal{N} \) = 4 SYM and ABJM and integrable Feynman graphs, JHEP03 (2018) 077 [arXiv:1612.05895] [INSPIRE].
V.V. Bazhanov, T. Lukowski, C. Meneghelli and M. Staudacher, A shortcut to the Q-operator, J. Stat. Mech.1011 (2010) P11002 [arXiv:1005.3261] [INSPIRE].
V.V. Bazhanov et al., Baxter Q-operators and representations of Yangians, Nucl. Phys.B 850 (2011) 148 [arXiv:1010.3699] [INSPIRE].
R. Frassek, T. Lukowski, C. Meneghelli and M. Staudacher, Oscillator construction of su(n|m) Q-operators, Nucl. Phys.B 850 (2011) 175 [arXiv:1012.6021] [INSPIRE].
R. Frassek, T. Lukowski, C. Meneghelli and M. Staudacher, Baxter operators and hamiltonians for ‘nearly all’ integrable closed \( \mathfrak{gl} \)(n) spin chains, Nucl. Phys.B 874 (2013) 620 [arXiv:1112.3600] [INSPIRE].
V. Kazakov, S. Leurent and Z. Tsuboi, Baxter’s Q-operators and operatorial Backlund flow for quantum (super)-spin chains, Commun. Math. Phys.311 (2012) 787 [arXiv:1010.4022] [INSPIRE].
R. Frassek, C. Marboe and D. Meidinger, Evaluation of the operatorial Q-system for non-compact super spin chains, JHEP09 (2017) 018 [arXiv:1706.02320] [INSPIRE].
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Marboe, C., Widén, E. The fate of the Konishi multiplet in the β-deformed Quantum Spectral Curve. J. High Energ. Phys. 2020, 26 (2020). https://doi.org/10.1007/JHEP01(2020)026
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DOI: https://doi.org/10.1007/JHEP01(2020)026