Correlators in the theory of Integral Discriminants

TL;DR

This paper explores invariant correlators in integral discriminants, proposing a differential operator method to compute them and revealing their polynomial nature, which hints at superintegrability in non-Gaussian integral models.

Contribution

It introduces a novel differential operator approach for calculating invariant correlators in integral discriminants, highlighting their polynomial structure and potential superintegrability.

Findings

Invariant correlators can be computed using differential operators.

Correlators often appear as polynomials in fundamental invariants.

The approach suggests a superintegrability phenomenon in the model.

Abstract

Integral discriminants provide a simple and fundamental model for non-Gaussian integrals, associated with homogeneous polynomials of degree r in n variables. We argue that, in this context, the study of correlators is equally if not more important. In this paper, we study a natural class of correlators in this model -- the invariant correlators. We suggest a general method to compute invariant correlators using differential operators that act on the partition function. This method allows to compute general invariant correlators in terms of the fundamental invariants. Moreover, in some cases the correlators appear to be simply polynomials in the invariants. This could be an interesting manifestation of superintegrability phenomenon in the theory of integral discriminants.