On the equivalence between real and superfield 5d formalisms

TL;DR

This paper proves the equivalence between two supersymmetric formalisms for five-dimensional theories, providing a dictionary to translate between the real formalism and the superfield formalism, clarifying their relationship.

Contribution

It explicitly demonstrates the equivalence and constructs a translation dictionary between the real and superfield formalisms for 5d supersymmetric theories.

Findings

Established the formal equivalence between the two formalisms.

Provided a systematic translation dictionary.

Clarified the relationship for practical use in literature.

Abstract

We explicitly prove the equivalence and construct a dictionary between two different supersymmetric formalisms for five-dimensional theories commonly used in the literature. One is the real formalism, which consists in doubling the number of degrees of freedom and then imposing reality constraints and the other is the usual superfield formalism.