Abstract
We quantize super Yang-Mills action in $\mathcal{N}=3$ harmonic superspace using "Fermi-Feynman" gauge and also develop the background field formalism. This leads to simpler propagators and Feynman rules that are useful in performing explicit calculations. The superspace rules are used to show that divergences do not appear at 1-loop and beyond. We also compute a finite contribution to the effective action from a 4-point diagram at 1-loop, which matches the expected covariant result.
Highlights
N 1⁄4 3 harmonic superspace in four dimensions was developed by GIKOS around three and a half decades ago [1,2], and it provided the first successful off-shell formulation of four-dimensional (4D) N 1⁄4 3 super YangMills (SYM) theory
It is well known that the field content of a N 1⁄4 3 vector multiplet is the same as that of a N 1⁄4 4 one, and Zupnik explicitly showed this hidden supersymmetry of the N 1⁄4 3 SYM in [4]
The N 1⁄4 3 superspace manifests the full superconformal symmetry, and using such symmetry arguments, low-energy effective action for N 1⁄4 3 and N 1⁄4 4 were considered by Zupnik and collaborators in [5–8]
Summary
N 1⁄4 3 harmonic superspace in four dimensions was developed by GIKOS around three and a half decades ago [1,2], and it provided the first successful off-shell formulation of four-dimensional (4D) N 1⁄4 3 super YangMills (SYM) theory This theory was quantized in “Landau” gauge a few years later by Delduc and McCabe [3]; the propagators obtained did not lend themselves to easier calculations. We choose “Fermi-Feynman” gauge to drastically reduce the number (9 → 1) and simplify the form (fchiral; antichiral; linearganalytic → just analytic) of propagators when compared to [3]. This simplifies the proof of the nonrenormalization theorem as one might expect.
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