Some results related to non-Abelian correlation inequalities for invariant observables

Date: 2022-08-11

Time: 09:30 - 10:30


Abdelmalek Abdesselam


When considering the GKS 2 inequality for invariant observables (inner products) of the O(N) model, a natural approach is to clear denominators, and prove the resulting inequality in a term-by-term manner in the expansion with respect to the ferromagnetic J couplings. This is what worked in the only settled cases N=1 and N=2. I revisited these term-by-term inequalities, which are with respect to the free invariant measure, and proved that a more general collection of inequalities is true in the limit of large powers of the observables. I treated both the O(N) and CP^{N-1} models for any strictly positive integer N. If time permits, I will discuss the problem of extending this result to real non-integer N’s.