Correlation Functions in Matrix Models Modified by Wormhole Terms

TL;DR

This paper investigates how adding wormhole-like trace-squared modifications to matrix models affects correlation functions, revealing new operator behaviors and extended Virasoro constraints in the context of minimal models and Liouville theory.

Contribution

It introduces a modified matrix model framework with trace-squared terms, demonstrating their impact on correlation functions and operator dressing, extending existing theoretical understanding.

Findings

Correlation functions satisfy modified Virasoro constraints.

Dressed order parameters follow Goulian-Li formulae with negative Liouville exponents.

Supports the existence of operators with negative gravitational dressing in modified models.

Abstract

We calculate correlation functions in matrix models modified by trace-squared terms. First we study scaling operators in modified one-matrix models and find that their correlation functions satisfy modified Virasoro constraints. Then we turn to dressed order parameters in minimal models and show that their correlators satisfy Goulian-Li formulae continued to negative Liouville dressing exponents. Our calculations provide additional support for the idea that the modified matrix models contain operators with the negative branch of gravitational dressing.