Virasoro representations with central charges $\frac{1}{2}$ and 1 on the real neutral fermion Fock space $F^{\otimes \frac{1}{2}}$

Abstract

We study a family of fermionic oscillator representations of the Virasoro algebra via 2-point-local Virasoro fields on the Fock space $F^{\otimes \frac{1}{2}}$ of a neutral (real) fermion. We obtain the decomposition of $F^{\otimes \frac{1}{2}}$ as a direct sum of irreducible highest weight Virasoro modules with central charge $c=1$. As a corollary we obtain the decomposition of the irreducible highest weight Virasoro modules with central charge $c=\frac{1}{2}$ into irreducible highest weight Virasoro modules with central charge $c=1$. As an application we show how positive sum (fermionic) character formulas for the Virasoro modules of charge $c=\frac{1}{2}$ follow from these decompositions.

Submitted to the Proceedings of the 22nd International Conference on Integrable Systems and Quantum symmetries, Prague, Czech Republic

References in corpus (4)

• Fermionic Sum Representations for Conformal Field Theory Characters
• Virasoro character identities from the Andrews--Bailey construction
• Andrews-Gordon identities from combinations of Virasoro characters
• Factorized Combinations of Virasoro Characters