Cluster expansion and resurgence in Polyakov model

Understand

In Polyakov model, a non-perturbative mass gap is formed at leading order semi-classics by instanton effects.

• By using the notions of critical points at infinity, cluster expansion and Lefschetz thimbles, we show that a third order effect in semi-classics gives an imaginary ambiguous contribution to mass gap, which is supposed to be real and unambiguous.
• This is troublesome for the original analysis, and it is difficult to resolve this issue directly in QFT.
• However, we find a new compactification of Polyakov model to quantum mechanics, by using a background 't Hooft flux (or coupling to TQFT).