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D. Correa, J. Maldacena and A. Sever, The quark anti-quark potential and the cusp anomalous dimension from a TBA equation , JHEP 08
Original
1913
Earlier work this paper cites.
V. K. Dobrev et al., Harmonic analysis on the n-dimensional lorentz group and its application to conformal quantum field theory , Lect.Notes Phys. 63 12
1977
Earlier work this paper cites.
A. B. Zamolodchikov, ’FISHNET’ DIAGRAMS AS A COMPLETELY INTEGRABLE SYSTEM , Phys. Lett. 97B
1980
Earlier work this paper cites.
T. Banks and A. Zaks, On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions , Nucl. Phys. B196
1982
Earlier work this paper cites.
L. N. Lipatov, High energy asymptotics of multi-color QCD and exactly sol vable lattice models , JETP Lett. 59 (1994) 596-599; 12
1994
Earlier work this paper cites.
R. G. Leigh and M. J. Strassler, Exactly marginal operators and duality in four-dimensional N=1 supersymmetric gauge theory , Nucl. Phys. B447
1995
Earlier work this paper cites.
L. D. Faddeev and G. P. Korchemsky, High-energy QCD as a completely integrable model , Phys. Lett. B342
1995
Earlier work this paper cites.
P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory , Graduate Texts in Contemporary Physics. Springer-Verlag, New York, 1997, 10.1007/978-1-4612-2256-9
1997
Earlier work this paper cites.
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity , Int. J. Theor. Phys. 38
1999
Earlier work this paper cites.
A. A. Tseytlin and K. Zarembo, Effective potential in nonsupersymmetric SU(N) x SU(N) gauge theory and interactions of type 0 D3-branes , Phys. Lett. B457
1999
Earlier work this paper cites.
E. Remiddi and J. A. M. Vermaseren, Harmonic polylogarithms , Int. J. Mod. Phys. A15
2000
Earlier work this paper cites.
S. E. Derkachov, G. P. Korchemsky and A. N. Manashov, Noncompact Heisenberg spin magnets from high-energy QCD: 1. Baxter Q operator and separation of variables , Nucl. Phys. B617
2001
Earlier work this paper cites.
H. J. De Vega and L. N. Lipatov, Interaction of reggeized gluons in the Baxter-Sklyanin representation , Phys. Rev. D64
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl. Phys. B599
2001
Earlier work this paper cites.
V. M. Braun, G. P. Korchemsky and D. Mueller, The Uses of conformal symmetry in QCD , Prog. Part. Nucl. Phys. 51
2003
Earlier work this paper cites.
F. C. S. Brown, Polylogarithmes multiples uniformes en une variable , Compt. Rend. Math. 338
2004
Earlier work this paper cites.
O. Lunin and J. M. Maldacena, Deforming field theories with U(1) x U(1) global symmetry and their gravity duals , JHEP 0505
2005
Earlier work this paper cites.
S. Frolov, Lax pair for strings in Lunin-Maldacena background , JHEP 05
2005
Earlier work this paper cites.
N. Beisert and R. Roiban, Beauty and the twist: The Bethe ansatz for twisted N=4 SYM , JHEP 08
2005
Earlier work this paper cites.
A. Dymarsky, I. R. Klebanov and R. Roiban, Perturbative search for fixed lines in large N gauge theories , JHEP 08
Original
2005
Earlier work this paper cites.

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2018

Exact Correlation Functions in Conformal Fishnet Theory

Gromov, Nikolay, Kazakov, Vladimir, Korchemsky, Gregory

Understand

We compute exactly various 4-point correlation functions of shortest scalar operators in bi-scalar planar four-dimensional "fishnet" CFT.

We apply the OPE to extract from these functions the exact expressions for the scaling dimensions and the structure constants of all exchanged operators with an arbitrary Lorentz spin.
In particular, we determine the conformal data of the simplest unprotected two-magnon operator analogous to the Konishi operator, as well as of the one-magnon operator.
We show that at weak coupling 4-point correlation functions can be systematically expanded in terms of harmonic polylogarithm functions and verify our results by explicit calculation of Feynman graphs at a few orders in the coupling.

Built on

D. Correa, J. Maldacena and A. Sever, The quark anti-quark potential and the cusp anomalous dimension from a TBA equation , JHEP 08
Original
1913
Earlier work this paper cites.
V. K. Dobrev et al., Harmonic analysis on the n-dimensional lorentz group and its application to conformal quantum field theory , Lect.Notes Phys. 63 12
1977
Earlier work this paper cites.
A. B. Zamolodchikov, ’FISHNET’ DIAGRAMS AS A COMPLETELY INTEGRABLE SYSTEM , Phys. Lett. 97B
1980
Earlier work this paper cites.
T. Banks and A. Zaks, On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions , Nucl. Phys. B196
1982
Earlier work this paper cites.
L. N. Lipatov, High energy asymptotics of multi-color QCD and exactly sol vable lattice models , JETP Lett. 59 (1994) 596-599; 12
1994
Earlier work this paper cites.
R. G. Leigh and M. J. Strassler, Exactly marginal operators and duality in four-dimensional N=1 supersymmetric gauge theory , Nucl. Phys. B447
1995
Earlier work this paper cites.
L. D. Faddeev and G. P. Korchemsky, High-energy QCD as a completely integrable model , Phys. Lett. B342
1995
Earlier work this paper cites.
P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory , Graduate Texts in Contemporary Physics. Springer-Verlag, New York, 1997, 10.1007/978-1-4612-2256-9
1997
Earlier work this paper cites.
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity , Int. J. Theor. Phys. 38
1999
Earlier work this paper cites.
A. A. Tseytlin and K. Zarembo, Effective potential in nonsupersymmetric SU(N) x SU(N) gauge theory and interactions of type 0 D3-branes , Phys. Lett. B457
1999
Earlier work this paper cites.
E. Remiddi and J. A. M. Vermaseren, Harmonic polylogarithms , Int. J. Mod. Phys. A15
2000
Earlier work this paper cites.
S. E. Derkachov, G. P. Korchemsky and A. N. Manashov, Noncompact Heisenberg spin magnets from high-energy QCD: 1. Baxter Q operator and separation of variables , Nucl. Phys. B617
2001
Earlier work this paper cites.
H. J. De Vega and L. N. Lipatov, Interaction of reggeized gluons in the Baxter-Sklyanin representation , Phys. Rev. D64
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl. Phys. B599
2001
Earlier work this paper cites.
V. M. Braun, G. P. Korchemsky and D. Mueller, The Uses of conformal symmetry in QCD , Prog. Part. Nucl. Phys. 51
2003
Earlier work this paper cites.
F. C. S. Brown, Polylogarithmes multiples uniformes en une variable , Compt. Rend. Math. 338
2004
Earlier work this paper cites.
O. Lunin and J. M. Maldacena, Deforming field theories with U(1) x U(1) global symmetry and their gravity duals , JHEP 0505
2005
Earlier work this paper cites.
S. Frolov, Lax pair for strings in Lunin-Maldacena background , JHEP 05
2005
Earlier work this paper cites.
N. Beisert and R. Roiban, Beauty and the twist: The Bethe ansatz for twisted N=4 SYM , JHEP 08
2005
Earlier work this paper cites.
A. Dymarsky, I. R. Klebanov and R. Roiban, Perturbative search for fixed lines in large N gauge theories , JHEP 08
Original
2005
Earlier work this paper cites.