TY - JOUR

T1 - On classification of extremal non-holomorphic conformal field theories

AU - Tener, James E.

AU - Wang, Zhenghan

N1 - Publisher Copyright:
© 2017 IOP Publishing Ltd.

PY - 2017/2/20

Y1 - 2017/2/20

N2 - Rational chiral conformal field theories are organized according to their genus, which consists of a modular tensor category C and a central charge c. A longterm goal is to classify unitary rational conformal field theories based on a classification of unitary modular tensor categories. We conjecture that for any unitary modular tensor category C, there exists a unitary chiral conformal field theory V so that its modular tensor category CV is C. In this paper, we initiate a mathematical program in and around this conjecture. We define a class of extremal vertex operator algebras with minimal conformal dimensions as large as possible for their central charge, and non-trivial representation theory. We show that there are finitely many different characters of extremal vertex operator algebras V possessing at most three different irreducible modules. Moreover, we list all of the possible characters for such vertex operator algebras with c ≤ 48.

AB - Rational chiral conformal field theories are organized according to their genus, which consists of a modular tensor category C and a central charge c. A longterm goal is to classify unitary rational conformal field theories based on a classification of unitary modular tensor categories. We conjecture that for any unitary modular tensor category C, there exists a unitary chiral conformal field theory V so that its modular tensor category CV is C. In this paper, we initiate a mathematical program in and around this conjecture. We define a class of extremal vertex operator algebras with minimal conformal dimensions as large as possible for their central charge, and non-trivial representation theory. We show that there are finitely many different characters of extremal vertex operator algebras V possessing at most three different irreducible modules. Moreover, we list all of the possible characters for such vertex operator algebras with c ≤ 48.

KW - conformal field theory

KW - modular tensor category

KW - vertex operator algebra

UR - http://www.scopus.com/inward/record.url?scp=85014362189&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aa59cd

DO - 10.1088/1751-8121/aa59cd

M3 - Article

AN - SCOPUS:85014362189

SN - 1751-8113

VL - 50

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 11

M1 - 115204

ER -