Back to Search
Start Over
Large N Limit of the O(N) Linear Sigma Model in 3D.
- Source :
- Communications in Mathematical Physics; Sep2022, Vol. 394 Issue 3, p953-1009, 57p
- Publication Year :
- 2022
-
Abstract
- In this paper we study the large N limit of the O(N)-invariant linear sigma model, which is a vector-valued generalization of the Φ 4 quantum field theory, on the three dimensional torus. We study the problem via its stochastic quantization, which yields a coupled system of N interacting SPDEs. We prove tightness of the invariant measures in the large N limit. For large enough mass or small enough coupling constant, they converge to the (massive) Gaussian free field at a rate of order 1 / N with respect to the Wasserstein distance. We also obtain tightness results for certain O(N) invariant observables. These generalize some of the results in Shen et al. (Ann Probab 50(1):131–202, 2022) from two dimensions to three dimensions. The proof leverages the method recently developed by Gubinelli and Hofmanová (Commun Math Phys 384(1):1–75, 2021) and combines many new techniques such as uniform in N estimates on perturbative objects as well as the solutions. [ABSTRACT FROM AUTHOR]
- Subjects :
- QUANTUM field theory
INVARIANT measures
COUPLING constants
TORUS
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 394
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 158629561
- Full Text :
- https://doi.org/10.1007/s00220-022-04414-w