Feynman Rules in N=2 Projective Superspace I: Massless hypermultiplets

TL;DR

This paper develops manifestly N=2 supersymmetric Feynman rules for massless hypermultiplets in projective superspace, ensuring correct component propagators and compatibility with dualities, advancing supersymmetric quantum field theory methods.

Contribution

It provides the first explicit construction of N=2 supersymmetric Feynman rules in projective superspace for massless hypermultiplets, including their reduction to N=1 superspace.

Findings

Correct component propagators obtained from Feynman rules

Compatibility with auxiliary field duality

Consistency with hypermultiplet-tensor multiplet duality

Abstract

Manifestly N=2 supersymmetric Feynman rules are found for different off-shell realizations of the massless hypermultiplet in projective superspace. When we reduce the Feynman rules to an N=1 superspace we obtain the correct component propagators. The Feynman rules are shown to be compatible with a ``duality'' that acts only on the auxiliary fields, as well as with the usual duality relating the hypermultiplet to the tensor multiplet.