Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies

Understand

Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals.

• The latter require a precise regularization to deal with the derivative interactions arising from the nonlinear kinetic term.
• Recently, for maximally symmetric spaces, simplified path integrals have been developed: they allow to trade the nonlinear kinetic term with a purely quadratic kinetic term (linear sigma model).
• This happens at the expense of introducing a suitable effective scalar potential, which contains the information on the curvature of the space.