# Exact correlators in the Gaussian Hermitian matrix model

## TL;DR

This paper derives new $W_{1+
abla}$ and Virasoro constraints for the Gaussian Hermitian matrix model, leading to an effective formula for correlators and revealing underlying algebraic structures.

## Contribution

It introduces $W_{1+
abla}$ constraints and a null 3-algebra structure, providing a novel method to compute correlators in the Gaussian Hermitian matrix model.

## Key findings

- Derived $W_{1+
abla}$ constraints and $W_{1+
abla}$ $n$-algebra.
- Established Virasoro constraints with null 3-algebra.
- Presented a new effective formula for correlators.

## Abstract

We present the $W_{1+\infty}$ constraints for the Gaussian Hermitian matrix model, where the constructed constraint operators yield the $W_{1+\infty}$ $n$-algebra. For the Virasoro constraints, we note that the constraint operators give the null 3-algebra. With the help of our Virasoro constraints, we derive a new effective formula for correlators in the Gaussian Hermitian matrix model.