2015/01/05 by Ricardo Couso-Santamaría, Ricardo Schiappa, Ricardo Vaz · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Gauge theory #Instanton #Mathematical physics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum chromodynamics #Resummation #cond-mat.stat-mech #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.aop.2015.02.019
34 pages, 15 figures, jheppub-nosort.sty
arxiv created 2015/01/05 · openalex publication_date 2015/02/19 · arxiv updated 2015/05/20 · openalex created_date 2022/10/02 · openalex updated_date 2026/04/04
Due to instanton effects, gauge-theoretic large N expansions yield asymptotic series, in powers of 1/N2. The present work shows how to generically make such expansions meaningful via their completion into resurgent transseries, encoding both perturbative and nonperturbative data. Large N resurgent transseries compute gauge-theoretic finite N results nonperturbatively (no matter how small N is). Explicit calculations are carried out within the gauge theory prototypical example of the quartic matrix model. Due to integrability in the matrix model, it is possible to analytically compute (fixed integer) finite N results. At the same time, the large N resurgent transseries for the free energy of this model was recently constructed. Together, it is shown how the resummation of the large N resurgent transseries matches the analytical finite N results up to remarkable numerical accuracy. Due to lack of Borel summability, Stokes phenomena has to be carefully taken into account, implying that instantons play a dominant role in describing the finite N physics. The final resurgence results can be analytically continued, defining gauge theory for any complex value of N.