THE HETEROTIC GREEN-SCHWARZ SUPERSTRING ON AN N=(2,0) SUPER WORLD-SHEET

By defining the heterotic Green-Schwarz superstring action on an N = (2,0) super world-sheet, rather than on an ordinary world-sheet, many problems with the interacting Green-Schwarz superstring forma ism can be solved. In the light-cone approach, superconformally transforming the light-cone super world-sheet onto an N = (2,0) super Riemann surface allows the elimination of the non-trivial interaction-point operators that complicate the evaluation of scattering amplitudes. In the Polyakov approach, the ten-dimensional heterotic Green-Schwarz covariant action defined on an N = (2,0) super world-sheet can be gauge-fixed to a free-field action with non-anomalous N = (2,0) superconformal invariance, and integrating the exponential of the covariant action over all punctured N = (2,0) super Riemann surfaces produces scattering amplitudes that closely resemble amplitudes obtained using the unitary light-cone approach.