Ding-Iohara-Miki symmetry of network matrix models

TL;DR

This paper explores the role of Ding-Iohara-Miki algebras in describing Ward identities in network matrix models, highlighting their significance as deformations of classical algebras for various deformed gauge theories.

Contribution

It establishes the connection between DIM algebras and Ward identities in network matrix models, extending to elliptic cases relevant for 6d gauge theories with adjoint matter.

Findings

DIM algebras describe Ward identities in network matrix models.

Deformations of Virasoro/W-algebras are realized through DIM and their limits.

Elliptic qq-characters are discussed in the context of these models.

Abstract

Ward identities in the most general "network matrix model" can be described in terms of the Ding-Iohara-Miki algebras (DIM). This confirms an expectation that such algebras and their various limits/reductions are the relevant substitutes/deformations of the Virasoro/W-algebra for (q, t) and (q_1, q_2, q_3) deformed network matrix models. Exhaustive for these purposes should be the Pagoda triple-affine elliptic DIM, which corresponds to networks associated with 6d gauge theories with adjoint matter (double elliptic systems). We provide some details on elliptic qq-characters.