We prove the Polyakov conjecture on the supertorus 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 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
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February 2000
Research Article|
February 01 2000
Polyakov conjecture on the supertorus
M. Kachkachi;
M. Kachkachi
Département de Mathématiques et Informatique, F.S.T. Settat, Université Hassan 1er, Settat, Morocco
UFR-HEP, Département de Physique, Faculté des Sciences, Université MV, Rabat, Morocco
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O. Dafounansou;
O. Dafounansou
UFR-HEP, Département de Physique, Faculté des Sciences, Université MV, Rabat, Morocco
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M. Nazah
M. Nazah
UFR-PTH, Département de Physiques, Faculté des Sciences, Université MV, Rabat, Morocco
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J. Math. Phys. 41, 891–897 (2000)
Article history
Received:
March 26 1998
Accepted:
November 12 1999
Citation
M. Kachkachi, O. Dafounansou, M. Nazah; Polyakov conjecture on the supertorus. J. Math. Phys. 1 February 2000; 41 (2): 891–897. https://doi.org/10.1063/1.533169
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