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Conformal Graphs as Twisted Partition Functions.

Manthos Karydas1, Songyuan Li2, Anastasios C Petkou2

  • 1Illinois Center for Advanced Studies of the Universe and Department of Physics, <a href="https://ror.org/05e94g991">University of Illinois</a>, 1110 West Green St., Urbana Illinois 61801, USA.

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Summary
This summary is machine-generated.

Conformal ladder graphs are linked to twisted partition functions of free massive complex scalars. This connection, observed in conformal fishnet models, reveals underlying free dynamics through algebraic relations.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Conformal Field Theory

Background:

  • Conformal ladder graphs appear in various quantum field theory contexts.
  • Understanding these graphs is crucial for studying scattering amplitudes and correlation functions.
  • Connections between different mathematical structures in physics often lead to new insights.

Purpose of the Study:

  • To establish a relationship between L-loop conformal ladder graphs and twisted partition functions.
  • To explore the emergence of these graphs in specific conformal fishnet models.
  • To identify the underlying physical system generating these conformal structures.

Main Methods:

  • Analyzing four-point functions in 2D and 4D conformal fishnet models.
  • Investigating twisted thermal two-point functions of free massive complex scalars.
  • Deriving algebraic and differential relations among conformal graphs.

Main Results:

  • A direct correspondence is shown between L-loop conformal ladder graphs and twisted partition functions in d=2L+1 dimensions.
  • These graphs are generated by the twisted thermal two-point function for all loop orders.
  • The relationship is rooted in a system of two decoupled harmonic oscillators with an imaginary chemical potential.
  • Algebraic and differential relations mirroring free dynamics were found.

Conclusions:

  • The study reveals a deep connection between conformal ladder graphs and scalar field theory partition functions.
  • This correspondence provides a new perspective on calculating and understanding conformal graph structures.
  • The identified underlying physical system offers a framework for further theoretical exploration.