Mass generation for the two dimensional O(N) Linear Sigma Model in the large N limit
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912852556644352 |
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| author | Delgadino, Matías G. Smith, Scott A. |
| author_facet | Delgadino, Matías G. Smith, Scott A. |
| contents | This work studies the $O(N)$ Linear Sigma Model on $\mathbb{R}^{2}$ 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 $\mathbb{R}^{2}$, quantified in the $2$-Wasserstein distance with a weighted $H^{1}(\mathbb{R}^{2})$ 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/Üstünel extension of Talagrand's inequality with some classical tools in Euclidean Quantum Field Theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_19630 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mass generation for the two dimensional O(N) Linear Sigma Model in the large N limit Delgadino, Matías G. Smith, Scott A. Probability Mathematical Physics Analysis of PDEs This work studies the $O(N)$ Linear Sigma Model on $\mathbb{R}^{2}$ 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 $\mathbb{R}^{2}$, quantified in the $2$-Wasserstein distance with a weighted $H^{1}(\mathbb{R}^{2})$ 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/Üstünel extension of Talagrand's inequality with some classical tools in Euclidean Quantum Field Theory. |
| title | Mass generation for the two dimensional O(N) Linear Sigma Model in the large N limit |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2601.19630 |