The Ponzano-Regge asymptotic of the supersymmetric 6jS symbols

TL;DR

This paper extends the Ponzano-Regge asymptotic analysis to supersymmetric 6jS symbols, revealing parity-dependent behaviors that impact quantum gravity models.

Contribution

It adapts Gurau's proof to supersymmetric symbols, highlighting how intrinsic parities affect asymptotic behavior and oscillation patterns.

Findings

Decay rates vary with parity

Oscillation angles are shifted by parity effects

Results are relevant for 3D Quantum Supergravity

Abstract

We adapt the Gurau's proof (2008) about the asymptotic limit of Ponzano-Regge formula to supersymmetric 6jS symbols according to their intrinsic parities alpha, beta, gamma. The behaviour at a large scaling shows significant differences depending on these parities. The decay is slowed and the angles of the oscillating parts in cosine are generally shifted or more altered.Our results should be relevant in 3-D Quantum Supergravity and Spin Foam models. PACS: 03.65.Fd Algebraic methods PACS: 04.60.-m Quantum gravity PACS: 11.30.Pb Supersymmetry MSC: 81Q60; 83D05.