Cosmological Constant in LQG Vertex Amplitude

TL;DR

This paper introduces a q-deformation of the Euclidean EPRL/FK vertex amplitude in Loop Quantum Gravity, revealing that its large-spin asymptotics reproduces the Regge action with a cosmological constant and connecting it to Chern-Simons theory.

Contribution

It proposes a novel q-deformation of the LQG vertex amplitude using Vassiliev invariants, linking quantum group techniques to cosmological constant inclusion.

Findings

Large-j asymptotics yields the Regge action with cosmological constant

Establishes a relation between q-deformed amplitude and Chern-Simons theory

Introduces a new approach to incorporate cosmological constant in LQG

Abstract

A new q-deformation of the Euclidean EPRL/FK vertex amplitude is proposed by using the evaluation of the Vassiliev invariant associated with a 4-simplex graph (related to two copies of quantum SU(2) group at different roots of unity) embedded in a 3-sphere. We show that the large-j asymptotics of the q-deformed vertex amplitude gives the Regge action with a cosmological constant. In the end we also discuss its relation with a Chern-Simons theory on the boundary of 4-simplex.