Abstract
We write down a vertical representation for the elliptic Ding-Iohara-Miki algebra, and construct an elliptic version of the refined topological vertex of Awata, Feigin and Shiraishi. We show explicitly that this vertex reproduces the elliptic genus of M-strings, and that it is an intertwiner of the algebra.
Highlights
This underlying algebra is established to be a q-deformed W1+∞ algebra [8], and in [9], it is conjectured to be the same W∞[μ] algebra used in the higher-spin AdS3/CFT2 holography [11] up to a u(1)-extension
We first write down a representation of the elliptic DIM algebra in analogy to the vertical representation of the usual DIM algebra, and we construct an elliptic version of the refined topological vertex
We constructed a vertical representation whose basis is labeled by one Young diagram for the elliptic DIM algebra at γ = 1, and based on it, we did a parallel work to [6] to build an elliptic vertex, whose VEV associated to certain class of representation webs reproduces the partition function of corresponding 6d N = (1, 0) SCFTs up to some factor independent of Coulomb branch
Summary
The elliptic genus of M-strings [20] can be computed from the refined topological string on a Calabi-Yau geometry specified by a toric diagram with its top and bottom external legs identified together. It can be interpreted as the instanton partition function of the corresponding 6d N = (1, 0) theory on R4 × T 2 with omega background twisting. First we have an overall factor which does not depend on λ or μ, i.e. terms in the first line of equation (2.1) combined with a similar factor from the contraction of Φ∗λ and Φμ, Gellip(γv, v2; q, t, p) := exp This is an elliptic version of the original overall factor G(γv1,v2; q,t) := exp. X±(z) =: x±n z−n, ψ±(z) =: ψn±z−n, n∈Z n∈Z the direct consequence of which is that ψ0± are no longer centers of the algebra
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