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We derive a one-parameter deformation of the refined topological vertex that, when used to compute non-periodic web diagrams, reproduces the six-dimensional topological string partition functions that are computed using the refined vertex and periodic web diagrams.
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 vert
We propose new topological vertex formalism for Type IIB $(p,q)$ 5-brane web with an O5-plane. We apply our proposal to 5d $mathcal{N}=1$ Sp(1) gauge theory with $N_f=0,1,8$ flavors to compute the topological string partition functions and check the
We clarify three aspects of non-compact elliptic genera. Firstly, we give a path integral derivation of the elliptic genus of the cigar conformal field theory from its non-linear sigma-model description. The result is a manifestly modular sum over a
We analyse the computation of the partition function of 5d $T_N$ theories in Higgs branches using the topological vertex. The theories are realised by a web of $(p,q)$ 5-branes whose dual description may be given by an M-theory compactification on a
We derive closed formulae for the first examples of non-algebraic, elliptic `leading singularities in planar, maximally supersymmetric Yang-Mills theory and show that they are Yangian-invariant.