A Macdonald refined topological vertex

Abstract

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.

arXiv comment48 pages, added introductory material and references, corrected typos, version to appear in Journal of Physics A Special Issue dedicated to Professor Petr Kulish

References in corpus (36)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Geometric Engineering of Quantum Field Theories
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Topological Vertex
• The Refined Topological Vertex
• Localization techniques in quantum field theories
• On AGT relation in the case of U(3)
• Instanton counting on blowup. I. 4-dimensional pure gauge theory
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Chern-Simons Theory and Topological Strings
• A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
• Matrix Models, Geometric Engineering and Elliptic Genera
• Les Houches lectures on matrix models and topological strings
• Refined BPS state counting from Nekrasov's formula and Macdonald functions
• Refined Topological Vertex and Instanton Counting
• A commutative algebra on degenerate CP^1 and Macdonald polynomials
• Quantum Algebraic Approach to Refined Topological Vertex
• Five-dimensional AGT Relation and the Deformed beta-ensemble
• Instanton counting, Macdonald function and the moduli space of D-branes
• Topological Strings and Nekrasov's formulas
• Notes on Ding-Iohara algebra and AGT conjecture
• Kernel function and quantum algebras
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• AGT, Burge pairs and minimal models
• BKP plane partitions
• Elliptic Virasoro Conformal Blocks
• Elliptic Ding-Iohara Algebra and the Free Field Realization of the Elliptic Macdonald Operator
• Free field constructions for the elliptic algebra ${\mathcal{A}}_{q,p}({\widehat{sl}}_2)$ and Baxter's eight-vertex model
• Higher AGT Correspondences, W-algebras, and Higher Quantum Geometric Langlands Duality from M-Theory
• Shifted Schur process and asymptotics of large random strict plane partitions
• Commutative Families of the Elliptic Macdonald Operator
• Refining the Shifted Topological Vertex
• Hall-Littlewood plane partitions and KP
• From topological strings to minimal models
• Elliptic Ding-Iohara Algebra and Commutative Families of the Elliptic Macdonald Operator

Cited by in corpus (11)

• Webs of W-algebras
• (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
• A slow review of the AGT correspondence
• Macdonald topological vertices and brane condensates
• An elliptic topological vertex
• Free field theory and observables of periodic Macdonald processes
• Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters
• Coloured refined topological vertices and parafermion conformal field theories
• Free field approach to the Macdonald process
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish