Refined Topological Vertex, Cylindric Partitions and the U(1) Adjoint Theory

Abstract

We study the partition function of the compactified 5D U(1) gauge theory (in the Omega-background) with a single adjoint hypermultiplet, calculated using the refined topological vertex. We show that this partition function is an example a periodic Schur process and is a refinement of the generating function of cylindric plane partitions. The size of the cylinder is given by the mass of adjoint hypermultiplet and the parameters of the Omega-background. We also show that this partition function can be written as a trace of operators which are generalizations of vertex operators studied by Carlsson and Okounkov. In the last part of the paper we describe a way to obtain (q,t) identities using the refined topological vertex.

40 Pages

References in corpus (2)

• The Refined Topological Vertex
• Crystal Model for the Closed Topological Vertex Geometry

Cited by in corpus (36)

• M-Strings
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• Refined stable pair invariants for E-, M- and [p,q]-strings
• On instantons as Kaluza-Klein modes of M5-branes
• On orbifolds of M-Strings
• Non-Lagrangian Theories from Brane Junctions
• Topological strings and 5d T_N partition functions
• Instantons on the 5-sphere and M5-branes
• M5-branes, toric diagrams and gauge theory duality
• M-strings, Elliptic Genera and N=4 String Amplitudes
• Changing the preferred direction of the refined topological vertex
• The general M5-brane superconformal index
• Quiver Matrix Model and Topological Partition Function in Six Dimensions
• Quantum vortices, M2-branes and black holes
• Flop Invariance of Refined Topological Vertex and Link Homologies
• Wilson surfaces in M5-branes
• Indices for 6 dimensional superconformal field theories
• Refined Hopf Link Revisited
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• Instantons and the 5D U(1) gauge theory with extra adjoint
• A Nekrasov-Okounkov formula for Macdonald polynomials
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• Asymptotic M5-brane entropy from S-duality
• Integrable structure of melting crystal model with two q-parameters
• BPS states, torus links and wild character varieties
• Extended $5d$ Seiberg-Witten Theory and Melting Crystal
• Modular properties of full 5D SYM partition function
• ADHM Wilson line defect indices
• Quasi-Hopf twist and elliptic Nekrasov factor
• Topological Field Theory Amplitudes for $A_{N-1}$ Fibration
• Brane Webs and Random Processes
• Periodic Schur Process, Cylindric Partitions and N=2* Theory
• A Representation-Theoretic Approach to $qq$-Characters
• Generalizations of Nekrasov-Okounkov Identity
• Refined Topological Vertex and Duality of Gauge Theories in Generic Omega Backgrounds
• Quiver matrix model of ADHM type and BPS state counting in diverse dimensions