Quantum algebraic approach to refined topological vertex

H. Awata*, B. Feigin, J. Shiraishi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

94 Scopus citations

Abstract

We establish the equivalence between the refined topological vertex of Iqbal- Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W 1+∞ introduced by Miki. Our construction involves trivalent intertwining operators ℙ and ℙ * associated with triples of the bosonic Fock modules. Resembling the topological vertex, a triple of vectors ∈ Z 2 is attached to each intertwining operator, which satisfy the Calabi-Yau and smoothness conditions. It is shown that certain matrix elements of ℙ and ℙ* give the refined topological vertex C λμν(t, q) of Iqbal-Kozcaz-Vafa. With another choice of basis, we recover the refined topological vertex C λμ ν(q, t) of Awata-Kanno. The gluing factors appears correctly when we consider any compositions of ℙ and ℙ*. The spectral parameters attached to Fock spaces play the role of the Kähler parameters.

Original languageEnglish
Article number041
JournalJournal of High Energy Physics
Volume2012
Issue number3
DOIs
StatePublished - 2012
Externally publishedYes

Keywords

  • Conformal and W symmetry
  • Quantum groups
  • Supersymmetric gauge theory
  • Topological strings

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