Abstract:Supersymmetric nonlinear sigma models arise in the theory of disordered systems and are expected to share key features with O(N)-type models. They also reveal surprising connections with probabilistic models such as the vertex-reinforced jump process and the arboreal gas, making them a rich testing ground linking supersymmetric field theory and probability. In my talk, I will consider a family of nonlinear sigma models on $\mathbb{Z}^{d}$ whose target space is the hyperbolic supermanifold $H^{2∣2+2n}$, $n \in \mathbb{N}$, introduced by Crawford as an extension of Zirnbauer's $H^{2∣2}$ model for disordered systems.
I will show the exponential decay of the two-point correlation function in the high-temperature regime $T \geq C n$, with $C>0$ a universal constant, for any $n \geq 1$ and in any dimension $d\geq1$. The proof is based on the reduction to a marginal fermionic theory and combines a high-temperature cluster expansion with bounds derived via Grassmann norms. Based on joint ongoing work with M. Disertori and J. Duràn Fernàndez.
Il seminario si svolgerà in presenza presso il Dipartimento di Matematica e Fisica, Via della Vasca Navale 84 aula B.
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