Reply to comment on "Lost in translation: topological singularities in group field theory"

TL;DR

This paper refutes a claim that Feynman graphs in 3D group field theory always represent pseudo manifolds, clarifying definitional differences and highlighting issues with the alternative construction proposed.

Contribution

It clarifies the distinction between definitions of pseudo manifolds and critiques the validity of the alternative construction in the context of Feynman rules.

Findings

The original claim is invalid due to definitional differences.

The proposed construction cannot be implemented via Feynman rules.

The paper emphasizes the importance of consistent definitions in topological analysis.

Abstract

In [1, arXiv:1102.1844] the author disputes the conclusion of our paper [2, arXiv:1006.0714]. He claims that the Feynman graphs of three dimensional group field theory always represent pseudo manifolds. However, [1] uses a different definition for pseudo manifolds. also, in order to apply the new definition, [1] proposes a construction which cannot be implemented in a path integral by Feynman rules. These two points invalidate the claims of [1].