Chiral effective potential in $\mathcal{N}=1\mathrm{/}2$ non-commutative Wess-Zumino model

We study a structure of holomorphic quantum contributions to the effective action for $\mathcal{N}=1\mathrm{/}2$ noncommutative Wess-Zumino model. Using the symbol operator techniques we present the one-loop chiral effective potential in a form of integral over proper time of the appropriate heat kernel. We prove that this kernel can be exactly found. As a result we obtain the exact integral representation of the one-loop effective potential. Also we study the expansion of the effective potential in a series in powers of the chiral superfield $\mathrm{\Phi }$ and derivative $D^2\mathrm{\Phi }$ and construct a procedure for systematic calculation of the coefficients in the series. We show that all terms in the series without derivatives can be summed up in an explicit form.