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The Ba{\l}aban variational problem in the non-linear sigma model
Wojciech Dybalski, Alexander Stottmeister, Yoh Tanimoto
https://arxiv.org/abs/2403.09800 h…

The Bałaban variational problem in the non-linear sigma model
The minimization of the action of a QFT with a constraint dictated by the block averaging procedure is an important part of Bałaban's approach to renormalization. It is particularly interesting for QFTs with non-trivial target spaces, such as gauge theories or non-linear sigma models on a lattice. We analyze this step for the $O(4)$ non-linear sigma model in two dimensions and demonstrate, in this case, how various ingredients of Bałaban's approach play together. First, using variational calc…