Abstract
We compute the two-loop effective Kähler potential in three-dimensional N=2 supersymmetric electrodynamics with Chern–Simons kinetic term for the gauge superfield. The effective action is constructed on the base of background field method with one parametric family of gauges. In such an approach, the quadratic part of quantum action mixes the gauge and matter quantum superfields yielding the complications in the computations of the loop supergraphs. To avoid this obstacle and preserve dependence on the gauge parameter we make a non-local change of quantum matter superfields after which the propagator is diagonalized, however the new vertices have appeared. We fix the suitable background and develop the efficient procedure of calculating the two-loop supergraphs with the new vertices. We compute the divergent and finite parts of the superfield effective action, find the two-loop effective Kähler potential and show that it does not depend on the gauge parameter.
Highlights
It is well known that the leading part of the low-energy effective action in the supersymmetric field models with chiral matter superfields is described by effective Kahler potential
The two-loop effective Kahler potential was computed for the three-dimensional Wess-Zumino model in N = 2 superspace [15] but it has not been studied in gauge-matter models which have much more interesting classical and quantum properties
Note that there is a broad discussion of the structure of moduli space of three-dimensional gauge theories with N = 2 supersymmetry including its Higgs branch, but the corresponding Kahler potential has never been computed explicitly in perturbation theory
Summary
It is well known that the leading part of the low-energy effective action in the supersymmetric field models with chiral matter superfields is described by effective Kahler potential (see, e.g., [1]). We compute two-loop effective Kahler potential in three-dimensional N = 2 supersymmetric quantum electrodynamics (SQED) with Chern-Simons kinetic term for the gauge superfield. This background obeys classical and quantum effective equations of motion up to one-loop order This guarantees that the two-loop effective Kahler potential computed in this model is gauge independent. We directly demonstrate that the obtained one- and two-loop quantum corrections to the effective Kahler potential are independent of α, confirming its gauge independence Another technical comment concerns the details of applications of the background field method at the two-loop order. When we perform the background quantum splitting the classical action acquires a number of terms which mix gauge and matter superfields at the quadratic order and make the propagator non-diagonal.
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