We study the quantization on the torus of the N=2 spinning particle coupled to spacetime gravity to obtain a worldline representation of the effective action of an arbitrary antisymmetric tensor field. This representation contains on top of the usual proper time a new modular parameter implementing the reduction to a single tensor field. Then we describe how to use it: (i) to calculate the first few Seeley-DeWitt coefficients for antisymmetric tensor fields of arbitrary rank in arbitrary dimensions, (ii) to derive exact duality relations, and (iii) to compute some correlation functions.