Heat kernel of non-minimal gauge field kinetic operators on Moyal plane

Abstract

We generalize the Endo formula originally developed for the computation of the heat kernel asymptotic expansion for non-minimal operators in commutative gauge theories to the noncommutative case. In this way, the first three non-zero heat trace coefficients of the non-minimal U(N) gauge field kinetic operator on the Moyal plane taken in an arbitrary background are calculated. We show that the non-planar part of the heat trace asymptotics is determined by U(1) sector of the gauge model. The non-planar 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 non-local gauge-fixing dependent singularities of the one-loop effective action that destroy the renormalizability of the U(N) model at one-loop level. The twisted-gauge transformation approach is discussed.

21 pages, misprints corrected

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Cited by in corpus (5)

• On space-time noncommutative theories at finite temperature
• Heat Trace Asymptotics on Noncommutative Spaces
• Spectral Action in Noncommutative Geometry
• A note on the heat kernel coefficients for nonminimal operators
• On space-time noncommutative U(1) model at high temperature