HEAT KERNEL OF NONMINIMAL GAUGE FIELD KINETIC OPERATORS ON MOYAL PLANE

Abstract

We generalize the Endo formula1 originally developed for the computation of the heat kernel asymptotic expansion for nonminimal operators in commutative gauge theories to the noncommutative case. In this way, the first three nonzero heat trace coefficients of the nonminimal U (N) gauge field kinetic operator on the Moyal plane taken in an arbitrary background are calculated. We show that the nonplanar part of the heat trace asymptotics is determined by U (1) sector of the gauge model. The nonplanar or mixed heat kernel coefficients are shown to be gauge-fixing dependent in any dimension of space–time. In the case of the degenerate deformation parameter the lowest mixed coefficients in the heat expansion produce nonlocal gauge-fixing dependent singularities of the one-loop effective action that destroy the renormalizability of the U (N) model at one-loop level. Such phenomenon was observed at first in Ref. 2 for spacelike noncommutative ϕ4 scalar and U (1) gauge theories. The twisted-gauge transformation approach is discussed.