2017/06/30 by Nikolay Gromov, Vladimir Kazakov, Gregory Korchemsky +2 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Central charge #Conformal field theory #Conformal map #Integrable system #Quantization (signal processing) #Quantum #Quantum many-body systems #Scaling #Scaling limit #Spin (aerodynamics) #Spins #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1007/jhep01(2018)095
71 pages, 14 figures
openalex created_date 2017/06/23 · arxiv created 2017/11/14 · openalex publication_date 2018/01/01 · arxiv updated 2018/02/14 · openalex updated_date 2026/08/05
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 ) where ϕ1 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.