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We consider the refined topological vertex of Iqbal et al, as a function of two parameters (x, y), and deform it by introducing Macdonald parameters (q, t), as in the work of Vuletic on plane partitions, to obtain a Macdonald refined topological vertex. In the limit q -> t, we recover the refined topological vertex of Iqbal et al. In the limit x -> y, we obtain a qt-deformation of the topological vertex of Aganagic et al. Copies of the vertex can be glued to obtain qt-deformed 5D instanton partition functions that have well-defined 4D limits and, for generic values of (q, t), contain infinite-towers of poles for every pole in the limit q -> t.
We test in $(A_{n-1},A_{m-1})$ Argyres-Douglas theories with $mathrm{gcd}(n,m)=1$ the proposal of Songs in arXiv:1612.08956 that the Macdonald index gives a refined character of the dual chiral algebra. In particular, we extend the analysis to higher
A string theoretic derivation is given for the conjecture of Hausel, Letellier, and Rodriguez-Villegas on the cohomology of character varieties with marked points. Their formula is identified with a refined BPS expansion in the stable pair theory of
We consider the matrix model of $U(N)$ refined Chern-Simons theory on $S^3$ for the unknot. We derive a $q$-difference operator whose insertion in the matrix integral reproduces an infinite set of Ward identities which we interpret as $q$-Virasoro co
We propose a concrete form of a vertex function, which we call O-vertex, for the intersection between an O5-plane and a 5-brane in the topological vertex formalism, as an extension of the work of arXiv:1709.01928. Using the O-vertex it is possible to
We present closed-form expressions of unrefined instanton partition functions for gauge groups of type $BCD$ as sums over Young diagrams. For $mathrm{SO}(n)$ gauge groups, we provide a fivebrane web picture of our formula based on the vertex-operator