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.

40 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 (16)

• What is an integrable quench?
• All point correlation functions in SYK
• Nonplanar Integrability
• Giant Gravitons - with Strings Attached (III)
• Giant Gravitons - with Strings Attached (II)
• A study of open strings ending on giant gravitons, spin chains and integrability
• Surprisingly Simple Spectra
• Classical Open String Integrability
• Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT${}_4$
• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Solving holographic defects
• The four-point function of determinant operators in $\mathcal{N}=4$ SYM
• Two-Loop Integrability of ABJM Open Spin Chain from Giant Graviton
• Giant magnons and non-maximal giant gravitons
• Conformal quantum mechanics & the integrable spinning Fishnet

Cited by in corpus (1)

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