TY - JOUR
T1 - Quantum algebraic approach to refined topological vertex
AU - Awata, H.
AU - Feigin, B.
AU - Shiraishi, J.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Conformal and W symmetry
KW - Quantum groups
KW - Supersymmetric gauge theory
KW - Topological strings
UR - http://www.scopus.com/inward/record.url?scp=84859590528&partnerID=8YFLogxK
U2 - 10.1007/JHEP03(2012)041
DO - 10.1007/JHEP03(2012)041
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AN - SCOPUS:84859590528
SN - 1126-6708
VL - 2012
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 3
M1 - 041
ER -