Heat kernel, effective action and anomalies in noncommutative theories

Abstract

Being motivated by physical applications (as the phi^4 model) we calculate the heat kernel coefficients for generalised Laplacians on the Moyal plane containing both left and right multiplications. We found both star-local and star-nonlocal terms. By using these results we calculate the large mass and strong noncommutativity expansion of the effective action and of the vacuum energy. We also study the axial anomaly in the models with gauge fields acting on fermions from the left and from the right.

21 pages, v2: references added

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Cited by in corpus (19)

• Induced Gauge Theory on a Noncommutative Space
• Heat kernel and number theory on NC-torus
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Quantum corrections to the noncommutative kink
• Noncommutative U(1) gauge theory from a worldline perspective
• On space-time noncommutative theories at finite temperature
• Construction of the effective action in nonanticommutative supersymmetric field theories
• An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions
• Renormalization on noncommutative torus
• Heat kernel expansion and induced action for the matrix model Dirac operator
• Nilpotent noncommutativity and renormalization
• One-loop effective potential in $\mathcal{N}=1/2$ generic chiral superfield model
• One-loop Photon's Effective Action in the Noncommutative Scalar QED${}_3$
• Heat kernel of non-minimal second-order operators
• Induced Gauge Theory on a Noncommutative Space
• Scattering approach for calculating one-loop effective action and vacuum energy
• On space-time noncommutative U(1) model at high temperature
• Heat kernel expansion and induced action for matrix models
• Geometry-Induced Vacuum Polarization and Mode Shifts in Maxwell-Klein-Gordon Theory