Integrability of conformal fishnet theory

A bstract We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed N = 4 SYM theory. We show that the transfer matrix “building” the fishnet graphs emerge...

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Vydané v:The journal of high energy physics Ročník 2018; číslo 1; s. 1 - 78
Hlavní autori: Gromov, Nikolay, Kazakov, Vladimir, Korchemsky, Gregory, Negro, Stefano, Sizov, Grigory
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2018
Springer Nature B.V
Springer
SpringerOpen
Predmet:
Bethe Ansatz
Chains
Classical and Quantum Gravitation
Conformal Field Theory
Coupling
Current carriers
Deformation
Elementary Particles
Graphs
High energy physics
Lattice Integrable Models
Mathematics
Measurement
Operators
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Scalars
Scaling
Scattering Amplitudes
String Theory
Lattice Integrable Models
Bethe Ansatz
Scattering Amplitudes
Conformal Field Theory
ISSN:1029-8479, 1126-6708, 1029-8479
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Shrnutí:A bstract We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed N = 4 SYM theory. We show that the transfer matrix “building” the fishnet graphs emerges from the R −matrix of non-compact conformal SU(2 , 2) Heisenberg spin chain with spins belonging to principal series representations of the four-dimensional conformal group. We demonstrate explicitly a relationship between this integrable spin chain and the Quantum Spectral Curve (QSC) of N = 4 SYM. Using QSC and spin chain methods, we construct Baxter equation for Q −functions of the conformal spin chain needed for computation of the anomalous dimensions of operators of the type tr( ϕ 1 J ) where ϕ 1 is one of the two scalars of the theory. For J = 3 we derive from QSC a quantization condition that fixes the relevant solution of Baxter equation. The scaling dimensions of the operators only receive contributions from wheel-like graphs. We develop integrability techniques to compute the divergent part of these graphs and use it to present the weak coupling expansion of dimensions to very high orders. Then we apply our exact equations to calculate the anomalous dimensions with J = 3 to practically unlimited precision at any coupling. These equations also describe an infinite tower of local conformal operators all carrying the same charge J = 3. The method should be applicable for any J and, in principle, to any local operators of bi-scalar theory. We show that at strong coupling the scaling dimensions can be derived from semiclassical quantization of finite gap solutions describing an integrable system of noncompact SU(2 , 2) spins. This bears similarities with the classical strings arising in the strongly coupled limit of N = 4 SYM.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1029-8479
1126-6708
1029-8479
DOI:10.1007/JHEP01(2018)095