Multiplicative expression for the coefficient in fermionic 3-3 relation

TL;DR

This paper presents a multiplicative formula for the proportionality coefficient in fermionic 3-3 relations related to Pachner move 3-3, expressed through Grassmann-Gaussian exponents and complex 2-cocycles.

Contribution

It introduces a novel multiplicative expression for the coefficient in fermionic 3-3 relations, enhancing understanding of these relations in topological quantum field theory.

Findings

Derived a multiplicative form for the coefficient in fermionic 3-3 relations.

Connected the coefficient to complex 2-cocycles and Grassmann-Gaussian exponents.

Provided a new perspective on fermionic relations in topological invariants.

Abstract

Recently, a family of fermionic relations were discovered corresponding to Pachner move 3-3 and parameterized by complex-valued 2-cocycles, where the weight of a pentachoron (4-simplex) is a Grassmann-Gaussian exponent. Here, the proportionality coefficient between Berezin integrals in the l.h.s. and r.h.s. of such relations is written in a form multiplicative over simplices.