2014/03/05 by Aleksey Cherman, Daniele Dorigoni, Cherman, Aleksey +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1403.1277
openalex publication_date 2014/03/05 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Resurgence theory implies that the non-perturbative (NP) and perturbative (P)\ndata in a QFT are quantitatively related, and that detailed information about\nnon-perturbative saddle point field configurations of path integrals can be\nextracted from perturbation theory. Traditionally, only stable NP saddle points\nare considered in QFT, and homotopy group considerations are used to classify\nthem. However, in many QFTs the relevant homotopy groups are trivial, and even\nwhen they are non-trivial they leave many NP saddle points undetected.\nResurgence provides a refined classification of NP-saddles, going beyond\nconventional topological considerations. To demonstrate some of these ideas, we\nstudy the SU(N) principal chiral model (PCM), a two dimensional\nasymptotically free matrix field theory which has no instantons, because the\nrelevant homotopy group is trivial. Adiabatic continuity is used to reach a\nweakly coupled regime where NP effects are calculable. We then use resurgence\ntheory to uncover the existence and role of novel `fracton' saddle points,\nwhich turn out to be the fractionalized constituents of previously observed\nunstable `uniton' saddle points. The fractons play a crucial role in the\nphysics of the PCM, and are responsible for the dynamically generated mass gap\nof the theory. Moreover, we show that the fracton-anti-fracton events are the\nweak coupling realization of 't Hooft's renormalons, and argue that the\nrenormalon ambiguities are systematically cancelled in the semi-classical\nexpansion. Our results motivate the conjecture that the semi-classical\nexpansion of the path integral can be geometrized as a sum over Lefschetz\nthimbles.\n