Super Yang-Mills with partially non-linear extended supersymmetry

TL;DR

This work analyzes 4D $N=2$ Super Yang–Mills with partial non-linear supersymmetry, realized by a goldstino in a Maxwell (Bagger–Galperin) multiplet and constrained to remove the chiral $N=1$ sector of the non-abelian multiplet. A mass-mediation approach yields the key constraint $X oldsymbol{ extPhi}=0$, which, when solved, produces a closed, recursive expression for the composite $oldsymbol{ extPhi}$ in terms of $W^oldsymbol{eta}$, $oldsymbol{ extLambda}_{oldsymbol{eta}}$, $X$, and an effective $R_{ ext{eff}}$. The bosonic sector shows that, unlike the abelian case, the non-abelian Born–Infeld structure does not automatically emerge; YM dynamics remain quadratic in field strengths, indicating limitations in transferring the Born–Infeld form to non-abelian sectors under partial non-linear SUSY alone. The results establish a framework for partially non-linear SUSY in non-abelian settings and outline directions for achieving higher-order interactions and richer matter content, such as hypermultiplets or separate SUSY-breaking sources.

Abstract

We discuss 4D N=2 non-abelian gauge theories where one supersymmetry is preserved while the other one is spontaneously broken and non-linearly realized. The goldstino resides in a Maxwell multiplet of the Bagger-Galperin type. We introduce appropriate constraints that eliminate the chiral N=1 superfield sector of the non-abelian N=2 multiplets and discuss the properties of the leading order Lagrangians.