Conformal graphs as twisted partition functions

Abstract

We show that a class of $L$-loop conformal ladder graphs correspond to twisted partition functions of free massive complex scalars in $d=2L+1$ dimensions. The graphs arise as four-point functions in certain two- and four-dimensional conformal fishnet models. The twisted thermal two-point function of the scalars is a generator of such conformal graphs for all loops. We argue that this correspondence is seeded by a system of two decoupled harmonic oscillators twisted by an imaginary chemical potential. We find a number of algebraic and differential relations among the conformal graphs which mirror the underlying free dynamics.

V1: LaTeX 6 pages, double column, 2 figures V2: LaTex 7 pages, two appendices with technical details added, few typos corrected. Matched published version

References in corpus (8)

• Generating series of all modular graph forms from iterated Eisenstein integrals
• Exponential suppression with four legs and an infinity of loops
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles
• Finite-size versus finite-temperature effects in the critical long-range $O(N)$ model
• Notes on massless scalar field partition functions, modular invariance and Eisenstein series
• Dispersion relations, knot polynomials and the $q$-deformed harmonic oscillator
• Virtual and real processes, the Källén function, and the relation to dilogarithms

Cited by in corpus (7)

• The thermal bootstrap for the critical O(N) model
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Conformal line defects at finite temperature
• Antipodal self-duality of square fishnet graphs
• Modular properties of massive scalar partition functions
• The thermal representation of conformal ladder integrals
• Hypergeometry from $\hat{\mathrm{P}}$-Symmetry: Feynman Integrals in One and Two Dimensions