C, P, and T of Braid Excitations in Quantum Gravity

TL;DR

This paper explores the discrete symmetries of four-valent braid excitations in quantum gravity, establishing a correspondence with C, P, T transformations and analyzing their invariance properties.

Contribution

It identifies seven unique discrete transformations of four-valent braids and maps them to C, P, T, and their combinations, revealing their invariance in braid interactions.

Findings

Seven discrete transformations of braids are identified.

Each CPT multiplet is characterized by a non-negative integer.

Braid interactions are invariant under C, P, and T.

Abstract

We study the discrete transformations of four-valent braid excitations of framed spin networks embedded in a topological three-manifold. We show that four-valent braids allow seven and only seven discrete transformations. These transformations can be uniquely mapped to C, P, T, and their products. Each CPT multiplet of actively-interacting braids is found to be uniquely characterized by a non-negative integer. Finally, braid interactions turn out to be invariant under C, P, and T.