Geodesic
Infrared Asymptotics of the Heat Kernel and Nonlocal Effective Action
Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 3, pp. 328-356

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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 field. 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 a new powerlike, renormalization-independent nonlocal 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.
Keywords: effective action, nonlocal field theories, Schwinger–DeWitt expansion. 
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     author = {A. O. Barvinsky and D. V. Nesterov},
     title = {Infrared {Asymptotics} of the {Heat} {Kernel} and {Nonlocal} {Effective} {Action}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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A. O. Barvinsky; D. V. Nesterov. Infrared Asymptotics of the Heat Kernel and Nonlocal Effective Action. Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 3, pp. 328-356. http://geodesic.mathdoc.fr/item/TMF_2005_143_3_a1/