NONPLANAR CONTRIBUTION TO THE EFFECTIVE ACTION IN NONCOMMUTATIVE FLAT MANIFOLDS

The nonplanar contribution to the effective action for massless scalar and vector fields on D– dimensional manifold with p compact noncommutative extra dimensions is calculated. The zeta function may not be regular at the origin. Thus, the related heat kernel trace has a logarithmic term in the short t asymptotic expansion. Consequences of this fact are briefly discussed.