| Abstract: |
| This talk will focus on the $O(N)$ Linear Sigma Model on $\R^{2}$ under a scaling dictated by the formal $1/N$ expansion. We show that in the large $N$ limit, correlations decay exponentially fast, where the acquired mass decays exponentially in
the inverse temperature. In fact, each marginal converges to a massive Gaussian Free Field (GFF) on $\R^{2}$, quantified in the $2$-Wasserstein distance with a weighted $H^{1}(\R^{2})$ cost function. In contrast to prior work on the torus via parabolic stochastic quantization, our results hold without restrictions on the coupling constants, allowing us to also obtain a massive GFF in a suitable double scaling limit. Our proof combines the Feyel/\Ust\unel extension of Talagrand`s inequality with some classical tools in Euclidean Quantum Field Theory. |
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