Brick wall diagrams as a completely integrable system

TL;DR

This paper extends the integrable fishnet theory to a new 'brick-wall' diagram structure, calculating its free energy in closed form and exploring related higher-dimensional models.

Contribution

It introduces the brick-wall diagram as a new integrable structure and adapts Zamolodchikov's method to compute its free energy explicitly.

Findings

Closed-form expression for free energy of brick-wall diagrams

Extension of integrable fishnet models to new diagram structures

Discussion of related models in higher dimensions

Abstract

We study the free energy of an integrable, planar, chiral and non-unitary four-dimensional Yukawa theory, the bi-fermion fishnet theory discovered by Pittelli and Preti. The typical Feynman-diagrams of this model are of regular "brick-wall"-type, replacing the regular square lattices of standard fishnet theory. We adapt A. B. Zamolodchikov's powerful classic computation of the thermodynamic free energy of fishnet graphs to the brick-wall case in a transparent fashion, and find the result in closed form. Finally, we briefly discuss two further candidate integrable models in three and six dimensions related to the brick wall model.