Title: The operator product expansion for Yang-Mills theories


Abstract:
Originally conceived by Wilson in 1969, the operator product expansion (OPE) 
has found a multitude of applications in high-energy physics, conformal field
theory and condensed matter systems. In the context of Euclidean \phi^4 
theory, it has recently been shown that the OPE is much better behaved 
than expected: instead of being just an asymptotic expansion, it converges 
for arbitrary finite separations of the operators (at least to all orders in 
perturbation theory). We generalise these results to (Euclidean) Yang-Mills
theories, including suitable Ward identities, and derive a formula for the 
recursive construction of the OPE coefficients. We also explain how these 
results could be used for a non-perturbative construction of Yang-Mills 
theory. The talk is based on 
arXiv:1511.09425
 and 
arXiv:1603.08012.