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Correlation functions of determinant operators in conformal fishnet theory

Authors :
Shahpo, Omar
Vescovi, Edoardo
Source :
JHEP 06 (2022) 070
Publication Year :
2021

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.<br />Comment: 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

Subjects

Subjects :
High Energy Physics - Theory

Details

Database :
arXiv
Journal :
JHEP 06 (2022) 070
Publication Type :
Report
Accession number :
edsarx.2110.09458
Document Type :
Working Paper
Full Text :
https://doi.org/10.1007/JHEP06(2022)070