We prove the Polyakov conjecture on the supertorus (ST2): We determine an iterative solution at any order of the superconformal Ward identity and we show that the Polyakov action that describes the (1,0) 2D(two-dimensional)-supergravity, resums this perturbative series. The resolution of the super-Beltrami equation for the Wess–Zumino field from which the Polyakov action is expressed, is done by using on the one hand the Cauchy kernel techniques on ST2 defined in H. Kachkachi and M. Kachkachi, Class. Quantum Grav. 11, 493 (1994) and on the other hand, the formalism developed in M. Kachkachi and S. Kouadik, J. Math. Phys. 38, 4336 (1997). Hence, we determine the n-points Green functions from the Polyakov action expressed as a functional integral of the Beltrami superfield μ̂.

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