Extended supersymmetry and BPS solutions in baby Skyrme models

Abstract

Abstract:We continue the investigation of supersymmetric extensions of baby Skyrme models in d = 2 + 1 dimensions. In a first step, we show that the CP(1) form of the baby Skyrme model allows for the same N = 1 SUSY extension as its O(3) formulation. Then we construct the N = 1 SUSY extension of the gauged baby Skyrme model, i.e., the baby Skyrme model coupled to Maxwell electrodynamics. In a next step, we investigate the issue of N = 2 SUSY extensions of baby Skyrme models. We find that all gauged and ungauged submodels of the baby Skyrme model which support BPS soliton solutions allow for an N = 2 extension such that the BPS solutions are one-half BPS states (i.e., annihilated by one-half of the SUSY charges). In the course of our investigation, we also derive the general BPS equations for completely general N = 2 supersymmetric field theories of (both gauged and ungauged) chiral superfields, and apply them to the gauged nonlinear sigma model as a further, concrete example.

Skyrme-like models and supersymmetry in3+1dimensions

“…This result is completely analogous to what happens in 2 + 1 dimensions between the CP 1 -model and the N = 2 BPS baby Skyrme model [22].…”

“…This situation is quite similar to what happens for the N = 2 SUSY extension of the baby Skyrme model [22]. We can ask now about the possibility of including a potential term.…”

Non-uniqueness of the supersymmetric extension of the O(3) σ-model

“…For example in [12][13][14] different supersymmetric extensions of the baby Skyrme model were proposed. However, the fermionic part of the supersymmetric models contains potentially dangerous higherderivative terms.…”

Fractional instantons and bions in the O(N) model with twisted boundary conditions

“…[127,128]. This model can be made supersymmetric [129][130][131][132]. A generalization of the model to R 1 × S 1 with twisted boundary condition is expected to admit BPS fractional instantons.…”