Correlation functions of determinant operators in conformal fishnet theory

TL;DR

This paper analyzes correlation functions of determinant operators in the conformal fishnet theory, providing explicit calculations and diagrammatic structures, and extends the field-theory approach to arbitrary order in small coupling constants.

Contribution

It generalizes a field-theory method to compute correlation functions of determinant operators in the fishnet theory at any order and analyzes their Feynman graph structures.

Findings

Explicit two-point functions of determinants and deformations

Diagrammatic structures of three- and four-point correlators

Resummation of diagrams using Bethe-Salpeter method

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.