# Introduction to modular property of affine alegebra and conformal vertex algebra

I wonder how modular property naturally arises in conformal theory. Is it obvious from physical viewpoint?

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## 1 Answer

Yes -- see Cardy's paper Operator content of two-dimensional conformally invariant theories. In a nutshell, the torus partition function of a conformal theory can be computed using a transfer matrix in several ways. The equivalence of these different calculations is the modular invariance of the torus partition function.

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