BPS States in Supersymmetric Chiral Models with Higher Derivative Terms

TL;DR

This paper explores higher derivative supersymmetric chiral models, revealing how BPS states and solitons are affected, and introduces new models and BPS conditions with potential implications for supersymmetric field theories.

Contribution

It constructs supersymmetric higher derivative models with arbitrary potentials, analyzes BPS states, and derives new BPS conditions for domain wall junctions.

Findings

Higher derivative corrections cancel for certain BPS states.

New 1/4 BPS conditions for domain wall junctions.

Supersymmetric extension of the Faddeev-Skyrme model without four time derivatives.

Abstract

We study the higher derivative chiral models with four supercharges and BPS states in these models. The off-shell Lagrangian generically includes higher powers of the auxiliary fields F which causes distinct on-shell branches associated with the solutions to the auxiliary fields equation. We point out that the model admits a supersymmetric completion of arbitrary higher derivative bosonic models of a single complex scalar field and an arbitrary scalar potential can be introduced even without superpotentials. As an example, we present a supersymmetric extension of the Faddeev-Skyrme model without four time derivatives, in contrast to the previously proposed supersymmetric Faddeev-Skyrme-like model containing four time derivatives. In general, higher derivative terms together with a superpotential result in deformed scalar potentials. We find that higher derivative corrections to 1/2 BPS domain walls and 1/2 BPS lumps are exactly canceled out while the 1/4 BPS lumps (as compact baby Skyrmions) depend on a characteristic feature of the higher derivative models. We also find a new 1/4 BPS condition for domain wall junctions which generically receives higher derivative corrections.