Quantum algebraic approach to refined topological vertex
Abstract
We establish the equivalence between the refined topological vertex of IqbalKozcazVafa and a certain representation theory of the quantum algebra of type W _{1+∞} introduced by Miki. Our construction involves trivalent intertwining operators Φ and Φ^{*} associated with triples of the bosonic Fock modules. Resembling the topological vertex, a triple of vectors ∈ {mathbb{Z}^2} is attached to each intertwining operator, which satisfy the CalabiYau and smoothness conditions. It is shown that certain matrix elements of Φ and Φ^{*} give the refined topological vertex C _{λ μν } ( t, q) of IqbalKozcazVafa. With another choice of basis, we recover the refined topological vertex C _{λ μ } ^{ ν } ( q, t) of AwataKanno. The gluing factors appears correctly when we consider any compositions of Φ and Φ^{*}. The spectral parameters attached to Fock spaces play the role of the Kähler parameters.
 Publication:

Journal of High Energy Physics
 Pub Date:
 March 2012
 DOI:
 10.1007/JHEP03(2012)041
 arXiv:
 arXiv:1112.6074
 Bibcode:
 2012JHEP...03..041A
 Keywords:

 Quantum Groups;
 Topological Strings;
 Conformal and W Symmetry;
 Supersymmetric gauge theory;
 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 27 pages