1303.0856 (Adam J Peterson)

Deformation of the O(3) sigma model leading to fixed size instantons    [PDF]

Adam J Peterson

We discuss instantons in the nonsupersymmetric CP(1) model with a small mass deformation m preserving a $U(1) x Z_2$ symmetry in the Lagrangian. The introduction of the mass term breaks the classical scale invariance and thus lifts the instanton size $\rho$ from the moduli space. We observe that the instanton action in this model is unstable at any finite instanton size $\rho$ not equal to zero. To remedy this we introduce a forth order derivative term in the Lagrangian to force the instanton action to diverge at small values of $\rho$. With this addition the instanton action exhibits a minimum at a finite instanton size, and thus the instanton is stabilized at particular non-zero value of the size $\rho$.

View original: http://arxiv.org/abs/1303.0856