Refined toric branes, surface operators and factorization of generalized Macdonald polynomials

TL;DR

This paper establishes new universal factorization identities for generalized Macdonald polynomials, linking them to refined topological string amplitudes, surface operators, and degenerate conformal field theory vertices, using matrix model and Ding-Iohara-Miki constraints.

Contribution

It introduces novel universal factorization formulas for generalized Macdonald polynomials and connects them to refined topological strings, gauge theory surface operators, and CFT vertex operators.

Findings

Derived new factorization identities for Macdonald polynomials.

Connected factorized expressions to refined topological string amplitudes.

Unified framework for Macdonald polynomials, topological strings, and gauge theory operators.

Abstract

We find new universal factorization identities for generalized Macdonald polynomials on the topological locus. We prove the identities (which include all previously known forumlas of this kind) using factorization identities for matrix model averages, which are themselves consequences of Ding-Iohara-Miki constraints. Factorized expressions for generalized Macdonald polynomials are identified with refined topological string amplitudes containing a toric brane on an intermediate preferred leg, surface operators in gauge theory and certain degenerate CFT vertex operators.