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Problem of changing gauge in Polyakov's theory: Relation between light-cone and conformal gauges.

The problem of the change of gauge in string theory is discussed in the context of the functional-integral formulation of the theory. The equivalence between the light-cone and conformal gauges is shown. By performing a proper change of variables in commuting and ghost fields in the functional integral of Polykov's theory, the string theory in the conformal gauge is obtained from the light-cone gauge-fixed theory. Finally, the problem of changing gauge has been generalized to the higher-genus surfaces. It has been shown that string theory in the conformal gauge is equivalent to the light-cone gauge-fixed theory of strings, for surfaces with an arbitrary number of handles.