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.

arXiv comment21 pages, misprints corrected

References in corpus (38)

• Noncommutative Perturbative Dynamics
• Heat kernel expansion: user's manual
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Space-Time Noncommutative Field Theories And Unitarity
• A Gravity Theory on Noncommutative Spaces
• Space/Time Non-Commutativity and Causality
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory
• Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
• Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars
• Deformed Coordinate Spaces; Derivatives
• Spin-Statistics and CPT Theorems in Noncommutative Field Theory
• Comments on noncommutative gravity
• Two-Loop Diagrams in Noncommutative ${\varphi }_4^4$ theory
• Twisted Gauge Theories
• The spectral action for Moyal planes
• Construction of $\theta$-Poincaré Algebras and their Invariants on ${\mathcal{M}}_{\theta }$
• Twist Symmetry and Gauge Invariance
• Non-commutative heat kernel
• Non-linear Vacuum Phenomena in Non-commutative QED
• Twist and Spin-Statistics Relation in Noncommutative Quantum Field Theory
• Remarks on twisted noncommutative quantum field theory
• Quantum noncommutative gravity in two dimensions
• The thermal heat kernel expansion and the one-loop effective action of QCD at finite temperature
• Twist to close
• Non-Commutative Geometry and Twisted Conformal Symmetry
• Twist-Deformed Supersymmetries in Non-Anticommutative Superspaces
• Vacuum expectation value asymptotics for second order differential operators on manifolds with boundary
• Twist as a Symmetry Principle and the Noncommutative Gauge Theory Formulation
• Twisted Conformal Symmetry in Noncommutative Two-Dimensional Quantum Field Theory
• Trouble with space-like noncommutative field theory
• Heat kernel and number theory on NC-torus
• Heat-Kernel Approach to UV/IR Mixing on Isospectral Deformation Manifolds
• Heat Kernel Asymptotics of Operators with Non-Laplace Principal Part
• Heat kernel for non-minimal operators on a Kahler manifold
• On the Heat Kernel in Covariant Background Gauge
• Heat Kernel for Spin-3/2 Rarita-Schwinger Field in General Covariant Gauge
• Background field quantization and non-commutative Maxwell theory

Cited by in corpus (6)

• 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
• Spectral action in noncommutative geometry: An example