Instantons and chiral anomaly in fuzzy physics

In continuum physics, there are important topological aspects like instantons, theta-terms and the axial anomaly. Conventional lattice discretizations often have difficulties in treating one or the other of these aspects. In this paper, we develop discrete quantum field theories on fuzzy manifolds using noncommutative geometry. Basing ourselves on previous treatments of instantons and chiral fermions (without fermion doubling) on fuzzy spaces and especially fuzzy spheres, we present discrete representations of theta-terms and topological susceptibility for gauge theories and derive axial anomaly on the fuzzy sphere. Our gauge field action for four dimensions is bounded by the modulus of the instanton number as in the continuum.

Note:

29 pages, 1 figure, LaTeX

gauge field theory: Yang-Mills
field theory: scalar
field theory: fermion
action
quantization
instanton: zero mode
Theta parameter
anomaly: axial
differential geometry: noncommutative
susceptibility: topological

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