Algebraic Structures of Quantum Projective Field Theory Related to Fusion and Braiding. Hidden Additive Weight

TL;DR

This paper investigates the algebraic structures in quantum projective field theory, revealing a new hidden additive weight and exploring its implications for fusion, braiding, and symmetries.

Contribution

It introduces the concept of a hidden additive weight in quantum projective field theory and explores its role in algebraic structures and symmetries.

Findings

Discovered a hidden additive weight as a new quantum number.

Characterized sl(2,C)-primary fields by projective weights and the hidden weight.

Analyzed algebraic structures like projective W-algebras and G-hypermultiplets.

Abstract

The interaction of various algebraic structures describing fusion, braiding and group symmetries in quantum projective field theory is an object of an investigation in the paper. Structures of projective Zamolodchikov al- gebras, their represntations, spherical correlation functions, correlation characters and envelopping QPFT-operator algebras, projective \"W-algebras, shift algebras, braiding admissible QPFT-operator algebras and projective G-hypermultiplets are explored. It is proved (in the formalism of shift algebras) that sl(2,C)-primary fields are characterized by their projective weights and by the hidden additive weight, a hidden quantum number discovered in the paper (some discussions on this fact and its possible relation to a hidden 4-dimensional QFT maybe found in the note by S.Bychkov, S.Plotnikov and D.Juriev, Uspekhi Matem. Nauk 47(3) (1992)[in Russian]). The special attention is paid to various constructions of projective G-hyper- multiplets (QPFT-operator algebras with G-symmetries).