Irregular matrix model with $\mathcal{W}$ symmetry

Abstract

We present the irregular matrix model which has contains ${\mathcal{W}}_3$ and Virasoro symmetry. The irregular matrix model is obtained using the colliding limit of the Toda field theories and produces the inner product between irregular modules of ${\mathcal{W}}_3$ symmetry. We evaluate the partition function using the flow equation which is the realization of the Virasoro and $\mathcal{W}$-symmetry.

arXiv comment16 pages, 1 figure; v2: minor corrections, discussion and references added; v3: minor changes, equation (3.3) corrected

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