Configuration space integral for longn–knots and the Alexander polynomial

There is a higher dimensional analogue of the perturbative Chern-Simons theory in the sense that a similar perturbative series as in 3 dimensions, which is computed via configuration space integral, yields an invariant of higher dimensional knots (Bott-Cattaneo-Rossi invariant).This invariant was constructed by Bott for degree 2 and by Cattaneo-Rossi for higher degrees.However, its feature is yet unknown.In this paper we restrict the study to long ribbon n-knots and characterize the Bott-Cattaneo-Rossi invariant as a finite type invariant of long ribbon n-knots introduced by Habiro-Kanenobu-Shima [10].As a consequence, we obtain a nontrivial description of the Bott-Cattaneo-Rossi invariant in terms of the Alexander polynomial.