Hexagonalization of Fishnet integrals. Part II. Overlaps and multi-point correlators

Author(s)

Olivucci, Enrico

• Document type: Journal article
• Source: Journal of High Energy Physics; v. N/A, n. 1, p. 50-pg., 2024-01-16.

Abstract

This work presents the building-blocks of an integrability-based representation for multi-point Fishnet Feynman integrals with any number of loops. Such representation relies on the quantum separation of variables (SoV) of a non-compact spin-chain with symmetry SO(1, 5) explained in the first paper of this series. The building-blocks of the SoV representation are overlaps of the wave-functions of the spin-chain excitations inserted along the edges of a triangular tile of Fishnet lattice. The zoology of overlaps is analyzed along with various worked out instances in order to achieve compact formulae for the generic triangular tile. The procedure of assembling the tiles into a Fishnet integral is presented exhaustively. The present analysis describes multi-point correlators with disk topology in the bi-scalar limit of planar gamma-deformed N = 4 SYM theory, and it verifies some conjectural formulae for hexagonalisation of Fishnets CFTs present in the literature. The findings of this work are suitable of generalization to a wider class of Feynman diagrams. (AU)

• FAPESP's process: 16/01343-7 - ICTP South American Institute for Fundamental Research: a regional center for theoretical physics
• Grantee: Nathan Jacob Berkovits
• Support Opportunities: Special Projects
• FAPESP's process: 19/24277-8 - Applications of quantum field theory
• Grantee: Pedro Gil Martins Vieira
• Support Opportunities: Research Projects - SPEC Program