Supplementary Notes on VOA and 2D SCFT
Abstract
Sections 2--3 of this note were prepared primarily for the author's private use, as a means of organizing the materials in (generally non-holomorphic) conformal field theory (CFT) on 2-dimensions in the language of the vertex operator algebra, and also of collecting subtle details. The choice of topics is intended to supplement introductory physics textbooks on the subject. Section 4 deals with (generally non-holomorphic) Type 0 CFTs in the language of vertex operator superalgebra (SVOA). Formulations of crossing symmetry and intertwining superoperators [resp. CFT vertex superoperators] of states in the Ramond (SVOA-twisted) sector [resp. the Ramond--Ramond sector] are presented by using two auxiliary parameters. The formulation allows systematic generalization to the class of simple current extensions characterized by four conditions: (1) the vanishing third cohomology, (2) skew-symmetric bimultiplicative form, (3) fixed-point-free action of simple currents, and (4) one additional condition described in the main text.
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BibTeX
@misc{watari2026supplementary,
title = {{Supplementary Notes on VOA and 2D SCFT}},
author = {Taizan Watari},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03725},
eprint = {2610.03725},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03725},
}
RIS
TY - UNPB
TI - Supplementary Notes on VOA and 2D SCFT
AU - Taizan Watari
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03725
UR - https://arxiv.org/abs/2610.03725
AB - Sections 2--3 of this note were prepared primarily for the author's private use, as a means of organizing the materials in (generally non-holomorphic) conformal field theory (CFT) on 2-dimensions in the language of the vertex operator algebra, and also of collecting subtle details. The choice of topics is intended to supplement introductory physics textbooks on the subject. Section 4 deals with (generally non-holomorphic) Type 0 CFTs in the language of vertex operator superalgebra (SVOA). Formulations of crossing symmetry and intertwining superoperators [resp. CFT vertex superoperators] of states in the Ramond (SVOA-twisted) sector [resp. the Ramond--Ramond sector] are presented by using two auxiliary parameters. The formulation allows systematic generalization to the class of simple current extensions characterized by four conditions: (1) the vanishing third cohomology, (2) skew-symmetric bimultiplicative form, (3) fixed-point-free action of simple currents, and (4) one additional condition described in the main text.
ER -