Correlation functions of determinant operators in conformal fishnet theory

Abstract

We consider scalar local operators of the determinant type in the conformal ``fishnet'' theory that arises as a limit of gamma-deformed $\mathcal{N}=4$ super Yang-Mills theory. We generalise a field-theory approach to expand their correlation functions to arbitrary order in the small coupling constants and apply it to the bi-scalar reduction of the model. We explicitly analyse the two-point functions of determinants, as well as of certain deformations with the insertion of scalar fields, and describe the Feynman-graph structure of three- and four-point correlators with single-trace operators. These display the topology of globe and spiral graphs, which are known to renormalise single-trace operators, but with ``alternating'' boundary conditions. In the appendix material we further investigate a four-point function of two determinants and the shortest bi-local single trace. We resum the diagrams by the Bethe-Salpeter method and comment on the exchanged OPE states.

arXiv comment40 pages, 6 figures; added footnotes 2, 4, 11 and 16, expanded on calculations in Section 3 and holography in Conclusion, minor comments; it matches published version

References in corpus (74)

• Harmonic Polylogarithms
• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Conformal Four Point Functions and the Operator Product Expansion
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• Baryons And Branes In Anti de Sitter Space
• Invasion of the Giant Gravitons from Anti-de Sitter Space
• HPL, a Mathematica implementation of the harmonic polylogarithms
• Giant Gravitons in Conformal Field Theory
• Lax Pair for Strings in Lunin-Maldacena Background
• Large branes in AdS and their field theory dual
• A toy model for the AdS/CFT correspondence
• Quantum spectral curve for AdS_5/CFT_4
• SUSY and Goliath
• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• What is an integrable quench?
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• Conformal Partial Waves: Further Mathematical Results
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• All point correlation functions in SYK
• Open Strings from N=4 Super Yang-Mills
• Integrable open spin chains from giant gravitons
• Baryon Spectra and AdS/CFT Correspondence
• Quantizing Open Spin Chains with Variable Length: an example from Giant Gravitons
• Reflecting magnons
• Vibration modes of giant gravitons
• Shape and holography: studies of dual operators to giant gravitons
• Nonplanar Integrability
• Giant Gravitons - with Strings Attached (III)
• Giant Gravitons - with Strings Attached (II)
• Strongly γ-deformed N=4 SYM as an integrable CFT
• Giant Gravitons - with Strings Attached (I)
• Integrability of Conformal Fishnet Theory
• A study of open strings ending on giant gravitons, spin chains and integrability
• Giant Gravitons, BPS bounds and Noncommutativity
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Exact Three-Point Functions of Determinant Operators in Planar N=4 Supersymmetric Yang-Mills Theory
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
• Surprisingly Simple Spectra
• Classical Open String Integrability
• Exact Correlation Functions in Conformal Fishnet Theory
• On a CFT limit of planar ${\gamma }_i$-deformed $\mathcal{N}=4$ SYM theory
• Dual Separated Variables and Scalar Products
• Exactly solvable magnet of conformal spins in four dimensions
• The structure of n-point functions of chiral primary operators in N=4 super Yang-Mills at one-loop
• Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT${}_4$
• The Holographic Fishchain
• Emergent Threebrane Lattices
• Separation of variables and scalar products at any rank
• Integrable Fishnet from $\gamma$-Deformed $\mathcal{N}=2$ Quivers
• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Thermodynamic Bethe Ansatz for Fishnet CFT
• A piece of cake: the ground-state energies in gamma_i-deformed N=4 SYM theory
• Absorption of closed strings by giant gravitons
• Quantum Fishchain in $Ad{S}_5$
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Hexagons and Correlators in the Fishnet Theory
• The spectrum of tachyons in AdS/CFT
• The Holographic Dual of Strongly γ-deformed N=4 SYM Theory: Derivation, Generalization, Integrability and Discrete Reparametrization Symmetry
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Scalar Insertions in Cusped Wilson Loops in the Ladders Limit of Planar N=4 SYM
• Structure constants of heavy operators in ABJM/ABJ Theory
• Functional Equations and Separation of Variables for Exact g-Function
• Integrable Subsectors from Holography
• Solving holographic defects
• Open Spin Chains from Determinant Like Operators in ABJM Theory
• The four-point function of determinant operators in $\mathcal{N}=4$ SYM
• Two-Loop Integrability of ABJM Open Spin Chain from Giant Graviton
• Inelastic Magnon Scattering
• Giant magnons and non-maximal giant gravitons
• Conformal quantum mechanics & the integrable spinning Fishnet
• One-point functions in $\beta$-deformed N = 4 SYM with defect

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