Abstract
We study the free energy of an integrable, planar, chiral and non-unitary four-dimensional Yukawa theory, the bi-fermion fishnet theory discovered by Pittelli and Preti. The typical Feynman-diagrams of this model are of regular “brick-wall”-type, replacing the regular square lattices of standard fishnet theory. We adapt A. B. Zamolodchikov’s powerful classic computation of the thermodynamic free energy of fishnet graphs to the brick-wall case in a transparent fashion, and find the result in closed form. Finally, we briefly discuss two further candidate integrable models in three and six dimensions related to the brick wall model.
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References
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
A.B. Zamolodchikov, ‘Fishing-net’ diagrams as a completely integrable system, Phys. Lett. B 97 (1980) 63 [INSPIRE].
M. D’Eramo, G. Parisi and L. Peliti, Theoretical predictions for critical exponents at the lambda point of bose liquids, Lett. Nuovo Cim. 2 (1971) 878 [INSPIRE].
D.I. Kazakov, Calculation of Feynman diagrams by the “uniqueness” method, Theor. Math. Phys. 58 (1984) 223 [INSPIRE].
Y.G. Stroganov, A new calculation method for partition functions in some lattice models, Phys. Lett. A 74 (1979) 116 [INSPIRE].
R.J. Baxter, The inversion relation method for some two-dimensional exactly solved models in lattice statistics, J. Statist. Phys. 28 (1982) 1 [INSPIRE].
R.J. Baxter, Solving models in statistical mechanics, Adv. Stud. Pure Math. 19 (1989) 95 [INSPIRE].
R.J. Baxter, The ‘Inversion relation’ method for obtaining the free energy of the chiral Potts model, Physica A 322 (2003) 407 [cond-mat/0212075] [INSPIRE].
S.V. Pokrovsky and Y.A. Bashilov, Star-triangle relations in the exactly solvable statistical models, Commun. Math. Phys. 84 (1982) 103.
M. Bousquet-Melou, A.J. Guttmann, W.P. Orrick and A. Rechnitzer, Inversion relations, reciprocity and polyominoes, math/9908123.
Ö. 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 [Addendum ibid. 117 (2016) 259903] [arXiv:1512.06704] [INSPIRE].
N. Beisert and R. Roiban, Beauty and the twist: The Bethe ansatz for twisted N = 4 SYM, JHEP 08 (2005) 039 [hep-th/0505187] [INSPIRE].
J. Caetano, Ö. Gürdoğan and V. Kazakov, Chiral limit of \( \mathcal{N} \) = 4 SYM and ABJM and integrable Feynman graphs, JHEP 03 (2018) 077 [arXiv:1612.05895] [INSPIRE].
A. Pittelli and M. Preti, Integrable fishnet from γ-deformed \( \mathcal{N} \) = 2 quivers, Phys. Lett. B 798 (2019) 134971 [arXiv:1906.03680] [INSPIRE].
D. Chicherin et al., Yangian Symmetry for Fishnet Feynman Graphs, Phys. Rev. D 96 (2017) 121901 [arXiv:1708.00007] [INSPIRE].
D. Chicherin, S. Derkachov and A.P. Isaev, Conformal group: R-matrix and star-triangle relation, JHEP 04 (2013) 020 [arXiv:1206.4150] [INSPIRE].
N. Gromov, V. Kazakov and G. Korchemsky, Exact Correlation Functions in Conformal Fishnet Theory, JHEP 08 (2019) 123 [arXiv:1808.02688] [INSPIRE].
N. Gromov et al., Integrability of Conformal Fishnet Theory, JHEP 01 (2018) 095 [arXiv:1706.04167] [INSPIRE].
C. Sieg and M. Wilhelm, On a CFT limit of planar γi-deformed \( \mathcal{N} \) = 4 SYM theory, Phys. Lett. B 756 (2016) 118 [arXiv:1602.05817] [INSPIRE].
D. Grabner, N. Gromov, V. Kazakov and G. Korchemsky, Strongly γ-Deformed \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory as an Integrable Conformal Field Theory, Phys. Rev. Lett. 120 (2018) 111601 [arXiv:1711.04786] [INSPIRE].
V. Kazakov, E. Olivucci and M. Preti, Generalized fishnets and exact four-point correlators in chiral CFT4, JHEP 06 (2019) 078 [arXiv:1901.00011] [INSPIRE].
S. Derkachov and E. Olivucci, Exactly solvable single-trace four point correlators in χCFT4, JHEP 02 (2021) 146 [arXiv:2007.15049] [INSPIRE].
C. Ahn and M. Staudacher, The Integrable (Hyper)eclectic Spin Chain, JHEP 02 (2021) 019 [arXiv:2010.14515] [INSPIRE].
J. Fokken, C. Sieg and M. Wilhelm, Non-conformality of γi-deformed N = 4 SYM theory, J. Phys. A 47 (2014) 455401 [arXiv:1308.4420] [INSPIRE].
V. Kazakov and E. Olivucci, The loom for general fishnet CFTs, JHEP 06 (2023) 041 [arXiv:2212.09732] [INSPIRE].
E. Pomoni and L. Rastelli, Large N Field Theory and AdS Tachyons, JHEP 04 (2009) 020 [arXiv:0805.2261] [INSPIRE].
S. Derkachov and E. Olivucci, Conformal quantum mechanics & the integrable spinning Fishnet, JHEP 11 (2021) 060 [arXiv:2103.01940] [INSPIRE].
M. Preti, STR: a Mathematica package for the method of uniqueness, Int. J. Mod. Phys. C 31 (2020) 2050146 [arXiv:1811.04935] [INSPIRE].
H. Au-Yang and J.H.H. Perk, The large N limits of the chiral Potts model, Physica A 268 (1999) 175 [math/9906029] [INSPIRE].
V.V. Bazhanov, A.P. Kels and S.M. Sergeev, Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs, J. Phys. A 49 (2016) 464001 [arXiv:1602.07076] [INSPIRE].
D. Bombardelli, S-matrices and integrability, J. Phys. A 49 (2016) 323003 [arXiv:1606.02949] [INSPIRE].
R. Shankar and E. Witten, The S Matrix of the Supersymmetric Nonlinear Sigma Model, Phys. Rev. D 17 (1978) 2134 [INSPIRE].
A.B. Zamolodchikov, Exact s Matrix of Quantum Sine-Gordon Solitons, JETP Lett. 25 (1977) 468 [INSPIRE].
O. Mamroud and G. Torrents, RG stability of integrable fishnet models, JHEP 06 (2017) 012 [arXiv:1703.04152] [INSPIRE].
B. Basso and L.J. Dixon, Gluing Ladder Feynman Diagrams into Fishnets, Phys. Rev. Lett. 119 (2017) 071601 [arXiv:1705.03545] [INSPIRE].
N. Gromov and A. Sever, Derivation of the Holographic Dual of a Planar Conformal Field Theory in 4D, Phys. Rev. Lett. 123 (2019) 081602 [arXiv:1903.10508] [INSPIRE].
R.M. Iakhibbaev and D.M. Tolkachev, Generalising holographic fishchain, arXiv:2308.08914.
B. Basso and D.-L. Zhong, Continuum limit of fishnet graphs and AdS sigma model, JHEP 01 (2019) 002 [arXiv:1806.04105] [INSPIRE].
Acknowledgments
We thank Matthias Volk for initial collaboration on this project. We are thankful to Changrim Ahn, Zoltan Bajnok and Lance Dixon for very useful discussions. Special thanks to Lance Dixon, Enrico Olivucci and Volodya Kazakov for very careful readings of our manuskript, and several valuable suggestions on references. This work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — Projektnummer 417533893/GRK2575 “Rethinking Quantum Field Theory”. This research was supported in part by grant NSF PHY-1748958 to the Kavli Institute for Theoretical Physics (KITP).
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Kade, M., Staudacher, M. Brick wall diagrams as a completely integrable system. J. High Energ. Phys. 2024, 50 (2024). https://doi.org/10.1007/JHEP01(2024)050
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DOI: https://doi.org/10.1007/JHEP01(2024)050