Conformal Graphs as Twisted Partition Functions

We show that a class of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>L</a:mi></a:math>-loop conformal ladder graphs are intimately related to twisted partition functions of free massive complex scalars in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>d</c:mi><c:mo>=</c:mo><c:mn>2</c:mn><c:mi>L</c:mi><c:mo>+</c:mo><c:mn>1</c:mn></c:mrow></c:math> 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 becomes a generator of conformal ladder 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 that mirror the underlying free dynamics. Published by the American Physical Society 2024