Fermionic Loops in Numerical Stochastic Perturbation Theory

In recent years the Numerical implementation of Stochastic Perturbation Theory (NSPT) was introduced, which was able to reach unprecedented high orders in perturbative expansions in Lattice Gauge Theories (LGT). Till now the main limitation of the method has been the quenched approximation, an inclusion of fermionic loops contributions missing. We can now fill this gap. Let us first of all remind the basics of the method. NSPT [1] comes (almost for free . . . ) as an application of the Stochastic Quantization scheme of Parisi and Wu [2]. We briefly sketch it in the context of LGT. The Cornell group showed [3] that a Langevin equation for LGT can be formulated as