Elsevier

Nuclear Physics B

Volume 270, 1986, Pages 186-204
Nuclear Physics B

Operator content of two-dimensional conformally invariant theories

https://doi.org/10.1016/0550-3213(86)90552-3Get rights and content

Abstract

It is shown how conformal invariance relates many numerically accessible properties of the transfer matrix of a critical system in a finite-width infinitely long strip to bulk universal quantities. Conversely, general properties of the transfer matrix imply constraints on the allowed operator content of the theory. We show that unitary theories with a finite number of primary operators must have a conformal anomaly number c < 1, and therefore must fall into the classification of Friedan, Qiu and Shenker. For such theories, we derive sum rules which constrain the numbers of operators with given scaling dimensions.

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