Comments on fluxes and Chern numbers in non-commutative gauge theories
نویسندگان
چکیده
We consider fluxes through planes in the background of codimension four non-BPS soliton solution in non-commutative gauge theory and encounter a paradox. Although this flux is almost always zero, the value of the flux varies with respect to changing the position of the plane. This suggests that the conservation of fluxes is a subtle notion in non-commutative gauge theories. We propose a slight modification to the definition of flux, and show that it evaluates to the correct values in several known examples of the non-commutative soliton solutions.
منابع مشابه
Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories
The axial anomaly in lattice gauge theories has topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which validates the Leibniz rule of exterior derivatives...
متن کاملBrs Cohomology and the Chern Character in Non-commutative Geometry
We establish a general local formula computing the topological anomaly of gauge theories in the framework of non-commutative geometry. MSC91: 19D55, 81T13, 81T50
متن کاملA note on Noncommutative Chern-Simons Theories
The three dimensional Chern-Simons theory on the noncommutative plane is considered. We show that the action is invariant under arbitrary (finite) gauge transformations and hence, we can relax the level quantization condition which we have in the usual (commutative) Chern-Simons theories. We also briefly discuss the case of the noncommutative torus.
متن کاملOn the quantum equivalence of commutative and noncommutative Chern-Simons theories at higher orders
We continue our investigation of the quantum equivalence between commutative and noncommutative Chern-Simons theories by computing the complete set of two-loop quantum corrections to the correlation function of a pure open Wilson line and an open Wilson line with a field strength insertion, on the noncommutative side in a covariant gauge. The conjectured perturbative equivalence between the fre...
متن کاملNoncommutative Chern-Simons terms and the noncommutative vacuum
It is pointed out that the space noncommutativity parameters θ in noncommutative gauge theory can be considered as a set of superselection parameters, in analogy with the θ-angle in ordinary gauge theories. As such, they do not need to enter explicitly into the action. A simple generic formula is then suggested to reproduce the Chern-Simons action in noncommutative gauge theory, which reduces t...
متن کامل