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.

%B Communications in Mathematical Physics %8 Mar %G eng %U https://doi.org/10.1007/s00220-019-03392-w %R 10.1007/s00220-019-03392-w %0 Report %D 2018 %T Observables in the equivariant A-model %A Bonechi, F. %A Cattaneo, A.S. %A Riccardo Iraso %A Maxim Zabzine %G eng %U https://arxiv.org/abs/1807.08659 %0 Journal Article %J Journal of High Energy Physics %D 2016 %T Comparing Poisson Sigma Model with A-model %A Bonechi, F. %A Cattaneo, A.S. %A Riccardo Iraso %XWe 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.

%B Journal of High Energy Physics %V 2016 %P 133 %8 Oct %G eng %U https://doi.org/10.1007/JHEP10(2016)133 %R 10.1007/JHEP10(2016)133