2019/12/12 by Nick Crawford, Crawford, Nick
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Particle physics theoretical and experimental studies #Probability (math.PR) #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.1912.05817
openalex publication_date 2019/12/12 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28
In this paper we study a family of nonlinear σ-models in which the target space is the super manifold H2|2N. These models generalize Zirnbauer's H2|2 nonlinear σ-model which has a number of special features for which we find analogs in the general case. For example, by supersymmetric localization, the partition function of the H2|2 model is a constants independent of the coupling constants. Here we show that for the H2|2N model, the partition function is a multivariate polynomial of degree N-1, increasing in each variable. We use these facts to provide estimates on the Fourier and Laplace transforms of the 't-field' when these models are specialized to ℤ2. From the bounds, we conclude the t-field exhibits polynomial decay of correlations and has fluctuations which are at least those of a massless free field.