In this paper we recover the non-perturbative partition function of 2D Yang–Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D Yang–Mills theory on surfaces with boundaries and corners in the Batalin–Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting–-the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces–-building blocks–-and choosing a convenient gauge-fixing on the pieces, and assembling back the partition function on the surface, one recovers the known non-perturbative answers for 2D Yang–Mills theory.

1 aIraso, Riccardo1 aMnev, P. uhttps://doi.org/10.1007/s00220-019-03392-w00359nas a2200121 4500008004100000245004300041210004200084100001600126700001900142700002000161700001900181856003700200 2018 eng d00aObservables in the equivariant A-model0 aObservables in the equivariant Amodel1 aBonechi, F.1 aCattaneo, A.S.1 aIraso, Riccardo1 aZabzine, Maxim uhttps://arxiv.org/abs/1807.0865900889nas a2200169 4500008004100000022001400041245004700055210004600102260000800148300000800156490000900164520044700173100001600620700001900636700002000655856004400675 2016 eng d a1029-847900aComparing Poisson Sigma Model with A-model0 aComparing Poisson Sigma Model with Amodel cOct a1330 v20163 aWe discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.

1 aBonechi, F.1 aCattaneo, A.S.1 aIraso, Riccardo uhttps://doi.org/10.1007/JHEP10(2016)133