Infrared asymptotics of the heat kernel and nonlocal effective action

We review recent results in the nonperturbative theory of the heat kernel and its late-time asymptotic properties responsible for the infrared behavior of the quantum effective action for massless theories. In particular, we derive a generalization of the Coleman-Weinberg potential for theories with an inhomogeneous background held. This generalization represents a new nonlocal, nonperturbative action accounting for the effects in a, transition domain between the space-time interior and its infinity. In four dimensions, these effects delocalize the logarithmic Coleman-Weinberg potential, while in d > 4, they are dominated by anew powerlike, renormalization-independent non local structure. We also consider the nonperturbative behavior of the heat kernel in a, curved space-time with an asymptotically flat geometry. In particular, we analyze the conformal properties of the heat kernel for a conformally invariant scalar field and discuss the problem of segregating the local cosmological term from the nonlocal effective action.