Abstract
It is known that anomalies can be expressed as a quantity in a short-time limit of the proper time (Schwinger parameter) in point-particle field theories. A natural extension of these expressions for the anomalies is given in the heterotic-string theory. It is shown that the gauge and gravitational anomalies in the heterotic-string theory can be expressed as a surface integral over the Schwinger parameter. The modular invariance of hexagon anomalies allows us to restrict the region of integration to the boundary of the fundamental region. This invariance also shows that the surface integral vanishes, i.e., hexagon gauge and gravitational anomalies are absent in the heterotic-string theory.
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