Diagrammatic Monte-Carlo for large-N non-Abelian lattice field theories based on the convergent weak-coupling expansion

27 Jun 2017, 12:40


Pavel Buividovich (Regensburg University)


We demonstrate that non-Abelian lattice field theories such as principal chiral model and pure lattice gauge theory in the large-N limit admit infrared-finite weak-coupling expansion in powers of coupling and logs of coupling, reminiscent of re-summed series in thermal field theory and resurgent trans-series without exponential terms. Such a double-series structure arises due to the bare mass term proportional to the coupling constant, which stems from the Jacobian in the path integral measure and is absent in the scale-invariant classical action. This term renders the perturbative expansion infrared-finite even for an infinite lattice size, which allows to sample it using Diagrammatic Monte-Carlo. On the exactly solvable example we demonstrate that this expansion incorporates the non-perturbative mass gap. We then develop a DiagMC algorithm for sampling planar diagrams in the principal chiral model and numerically demonstrate the convergence of our expansion for up to 12 leading orders, which is the practical limit set by the increasingly strong sign problem at high orders. We find reasonably good agreement with conventional Monte-Carlo, extrapolated to infinite N. Finally, we comment on the applicability of our approach to planar QCD at zero and finite density.

Primary author

Pavel Buividovich (Regensburg University)


Dr Ali Davody (Regensburg University)

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