Branched Polymer Revisited

TL;DR

This paper clarifies the correlation functions of branched polymers, revealing they align with a modified $^3$ theory with a mass insertion, explaining their 1/p^4 behavior and Hausdorff dimension four.

Contribution

It demonstrates that branched polymer correlation functions correspond to a modified $^3$ theory with a mass insertion, correcting previous assumptions.

Findings

Correlation functions match a modified $^3$ theory with a mass insertion

Two-point function behaves as 1/p^4, not 1/p^2

Hausdorff dimension of branched polymers is four

Abstract

We show that correlation functions for branched polymers correspond to those for $\phi^3$ theory with a single mass insertion, not those for the $\phi^3$ theory themselves, as has been widely believed. In particular, the two-point function behaves as 1/p^4, not as 1/p^2. This behavior is consistent with the fact that the Hausdorff dimension of the branched polymer is four.