How does Gauge Cooling Stabilize Complex Langevin?
Provides theoretical insights into gauge cooling for lattice field theory practitioners, but is incremental as it focuses on a simplified 1D case.
The paper studies gauge cooling in complex Langevin for one-dimensional periodic settings, deriving exact gauge transforms and showing that cooling helps localize distributions to prevent excursions from the real axis in SU(2) Polyakov loop models.
We study the mechanism of the gauge cooling technique to stabilize the complex Langevin method in the one-dimensional periodic setting. In this case, we find the exact solutions for the gauge transform which minimizes the Frobenius norm of link variables. Thereby, we derive the underlying stochastic differential equations by continuing the numerical method with gauge cooling, and thus provide a number of insights on the effects of gauge cooling. A specific case study is carried out for the Polyakov loop model in $SU(2)$ theory, in which we show that the gauge cooling may help form a localized distribution to guarantee there is no excursion too far away from the real axis.