Covariant quantization of string theories is developed in the context of conformal field theory and the BRST quantization procedure. The BRST method is used to covariantly quantize superstrings, and in particular to construct the vertex operators for string emission as well as the supersymmetry charge. The calculation of string loop diagrams is sketched. We discuss how conformal methods can be used to study string compactification and dynamics.

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Conformal invariance and unitarity severely limit the possible values of critical exponents in two-dimensional systems.

Covariant quantization of string theories is developed in the context of conformal field theory and the BRST quantization procedure. The BRST method is used to covariantly quantize superstrings, and in particular to construct the vertex operators for string emission as well as the supersymmetry charge. The calculation of string loop diagrams is sketched. We discuss how conformal methods can be used to study string compactification and dynamics.

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We show that the weak mixing angle 0 w is the same for continuously con-.netted classical vacua of the heterotic string which have chiral fermions in their massless spectra. We also show that the world-sheet quantum field theory for any classical vacuum with spacetime supersymmetry possesses an N=2 superconformal invariance.

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