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Abstract We introduce an R-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra \( {U}_{q,t}\left({\widehat{\widehat{\mathfrak{gl}}}}_1\right) \). This R-matrix acts on pairs of 3d Young diagrams and retains the nice symmetry of the DIM algebra under the permutation of three deformation parameters q, t−1 and \( \frac{t}{q} \). We...

Abstract We compute the topological partition function (twisted index) of \( \mathcal{N} \) = 2 U(N) Chern-Simons theory with an adjoint chiral multiplet on Σg × S1. The localization technique shows that the underlying Frobenius algebra is the equivariant Verlinde algebra which is obtained from the canonical quantization of the complex Chern-Simons theory regularized by U(1...

; Published 16 April 2018
Academic Editor: Anna Nowinska
Copyright © 2018 **Hiroaki** **Kanno** et al. This is an open access article distributed under the Creative Commons Attribution License, which permits

Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into network matrix models with the hidden Ding-Iohara-Miki (DIM) symmetry. This lifting is especially simple for what we call balanced networks. Then, the Ward identities (known under the names of Virasoro/\( \mathcal{W} \)-constraints...

Abstract \( \mathrm{\mathcal{R}} \)-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. Calculation is straightforward and significantly simpler than the one through the universal \( \mathrm{\mathcal{R}} \)-matrix used for a similar calculation in the Yangian case by A. Smirnov but less general. We investigate the interplay between the...

We formulate the path integral description of the open superstring in which both orientable and nonorientable surfaces are taken into account. The vacuum energy is evaluated at the one-loop and by an invariance argument it is shown to vanish for the annulus and Möbius strip.