Grand-Canonical Symmetric Orbifold Theories

Abstract: In this letter, we study grand-canonical symmetric orbifolds of conformal field theories on the sphere. We show that a consistent operator product expansion can be defined, provided the Hilbert space is taken to be the direct sum of symmetric orbifolds of all degrees. This Hilbert space contains a tower of central operators of conformal dimension zero, one of which represents the central charge of the Virasoro algebra. Our construction thus provides a conformal field theory interpretation of the central charge operator $\mathcal{I}$ in $AdS_3$ string theory.