Conformal ladder integrals are represented via thermal free energies of massive scalars, obey a second-order differential equation in even dimensions at any loop order, and admit an all-loop resummation for arbitrary D.
Exponential suppression with four legs and an infinity of loops
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abstract
The L-loop 4-point ladder diagram of massless phi^3 theory is finite when all 4 legs are off-shell and is given in terms of polylogarithms with orders ranging from L to 2L. We obtain the exact solution of the linear Dyson-Schwinger equation that sums these ladder diagrams and show that this sum vanishes exponentially fast at strong coupling.
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A thermal representation for conformal ladder integrals
Conformal ladder integrals are represented via thermal free energies of massive scalars, obey a second-order differential equation in even dimensions at any loop order, and admit an all-loop resummation for arbitrary D.