Derivative Expansion and the Effective Action for the Abelian Chern-Simons Theory at Higher Orders

Abstract

We study systematically the higher order corrections to the parity violating part of the effective action for the Abelian Chern-Simons theory in 2+1 dimensions, using the method of derivative expansion. We explicitly calculate the parity violating parts of the quadratic, cubic and the quartic terms (in fields) of the effective action. We show that each of these actions can be summed, in principle, to all orders in the derivatives. However, such a structure is complicated and not very useful. On the other hand, at every order in the powers of the derivatives, we show that the effective action can also be summed to all orders in the fields. The resulting actions can be expressed in terms of the leading order effective action in the static limit. We prove gauge invariance, both large and small of the resulting effective actions. Various other features of the theory are also brought out.

36 pages

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Cited by in corpus (6)

• Induced higher-derivative Lorentz-violating Chern-Simons term at finite temperature
• Dirac electrons and domain walls: a realization in junctions of ferromagnets and topological insulators
• Parity Violating Bosonic Loops at Finite Temperature
• Induced parity violating thermal effective action for (2+1)-dimensional fermions interacting with a non-Abelian background
• Radiative corrections to the Chern-Simons term at finite temperature in the noncommutative Chern-Simons-Higgs model
• Non-Abelian Thermal Large Gauge Transformations in 2+1 Dimensions