arXiv:hep-th/0311155v2 18 Dec 2003 YITP-SB-03-55 Instanton Calculations for N = 1 2 super Yang-Mills Theory P.A. Grassi a,b, 1 , R. Ricci a, 2 , and D. Robles-Llana a, 3 (a) C.N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, NY 11794-3840, USA (b) Dipartimento di Scienze, Universit` a del Piemonte Orientale, C.so Borsalino 54, Alessandria, 15100, ITALY We study (anti-) instantons in super Yang-Mills theories defined on a non anticom- mutative superspace. The instanton solution that we consider is the same as in ordinary SU (2) N = 1 super Yang-Mills, but the anti-instanton receives corrections to the U (1) part of the connection which depend quadratically on fermionic coordinates, and linearly on the deformation parameter C . By substituting the exact solution into the classical Lagrangian the topological charge density receives a new contribution which is quadratic in C and quartic in the fermionic zero-modes. The topological charge turns out to be zero. We perform an expansion around the exact classical solution in presence of a fermionic background and calculate the full superdeterminant contributing to the one-loop partition function. We find that the one-loop partition function is not modified with respect to the usual N = 1 super Yang-Mills. Revised 12/8/2003 1 pgrassi@insti.physics.sunysb.edu 2 rricci@grad.physics.sunysb.edu 3 daniel@insti.physics.sunysb.edu