Operator Product Formulas in the Algebraic Approach of the Refined Topological Vertex
CAI Li-Qiang, WANG Li-Fang** , WU Ke, YANG Jie
School of Mathematical Sciences, Capital Normal University, Beijing 100048
Abstract :The refined topological vertex of Iqbal–Koz?az–Vafa has been investigated from the viewpoint of the quantum algebra of type W 1+∞ by Awata, Feigin, and Shiraishi. They introduced the trivalent intertwining operator ? which is normal ordered along with some prefactors. We manage to establish formulas from the infinite operator product of the vertex operators and the generalized ones to restore this prefactor, and obtain an explicit formula for the vertex realization of the topological vertex as well as the refined topological vertex.
收稿日期: 2012-10-26
出版日期: 2013-03-02
:
03.70.+k
(Theory of quantized fields)
11.25.Hf
(Conformal field theory, algebraic structures)
02.10.Ox
(Combinatorics; graph theory)
[1] Awata H, Feigin B and Shiraishi J 2011 arXiv:1112.6074[hep-th] [2] Iqbal A, Koz?az C and Vafa C 2009 J. High Energy Phys. 10 069 [3] Eguchi T and Kanno H 2003 J. High Energy Phys. 12 006 [4] Dimofte T and Gukov S 2010 Lett. Math. Phys. 91 1 [5] Awata H and Kanno H 2005 J. High Energy Phys. 0505 039 [6] Awata H and Kanno H 2009 Internat. J. Mod. Phys. A24 2253 [7] Macdonald I G 1995 Symmetric Functions and Hall Polynomials (Oxford: Oxford University) [8] Aganagic M, Klemm A, Marino M and Vafa C 2005 Commun. Math. Phys. 254 425 [9] Feigin B, Hashizume K, Hoshino A, Shiraishi J and Yanagida S 2009 J. Math. Phys. 50 095215 [10] Taki M 2008 J. High Energy Phys. 0803 048 [11] Miki K 2007 J. Math. Phys. 48 123520 [12] Nakajima H and Yoshioka K 2003 arXiv:0311058v1[math.AG] [13] Ding J and Iohara K 1997 Lett. Math. Phys. 41 181 [14] Feigin B, Feigin E, Jimbo M, Miwa T and Mukhin E 2011 Kyoto J. Math. 51 337 [15] Feigin B, Feigin E, Jimbo M, Miwa T and Mukhin E 2011 Kyoto J. Math. 51 365 [16] Feigin B and Tsymbaliuk A 2009 arXiv:0904.1679v1[math.RT] [17] Iqbal A and Kozcaz C 2011 arXiv:1111.0525v1[hep-th] [18] Mironov A, Morozov A and Shakirov S 2011 J. High Energy Phys. 1102 067 [19] Nakajima H and Yoshioka K 2005 Invent. Math. 162 313 [20] Nakajima H and Yoshioka K 2005 Transform. Groups 10 489 [21] Nekrasov N 2003 Adv. Theor. Math. Phys. 7 831 [22] Okounkov A and Reshetikhin N 2007 Commun. Math. Phys. 269 571 [23] Okounkov A, Reshetikhin N and Vafa C 2003 arXiv:0309208v2[hep-th] [24] Schiffmann O and Vasserot O 2012 arXiv:0905.2555v3[math.QA] [25] Feigin B, Jimbo M, Miwa T and Mukhin E 2011 arXiv:1110.5310v1 [math.QA]
[1]
. [J]. 中国物理快报, 2022, 39(12): 126301-.
[2]
. [J]. 中国物理快报, 2020, 37(1): 17801-017801.
[3]
. [J]. 中国物理快报, 2014, 31(10): 100401-100401.
[4]
. [J]. 中国物理快报, 2014, 31(03): 34202-034202.
[5]
. [J]. Chin. Phys. Lett., 2012, 29(11): 110303-110303.
[6]
RONG Shu-Jun**;LIU Qiu-Yu
. Flavor State of the Neutrino: Conditions for a Consistent Definition [J]. 中国物理快报, 2011, 28(12): 121401-121401.
[7]
ZHANG Xue;ZHENG Tai-Yu**;TIAN Tian;PAN Shu-Mei**
. The Dynamical Casimir Effect versus Collective Excitations in Atom Ensemble [J]. 中国物理快报, 2011, 28(6): 64202-064202.
[8]
CHENG Hong-Bo. The Casimir Force between Parallel Plates in Randall--Sundrum I Model [J]. 中国物理快报, 2010, 27(3): 31101-031101.
[9]
GENG Zhen-Duo;JIA Ning;ZHAO Xu;XIA Tian-Yu;JING Hui. Adiabatic Fidelity of Coherent Atom-Heteronuclear Molecule Conversion [J]. 中国物理快报, 2010, 27(3): 30303-030303.
[10]
XIONG Ai-Min;CHEN Xiao-Song. Casimir Force of Piston Systems with Arbitrary Cross Sections under Different Boundary Conditions [J]. 中国物理快报, 2009, 26(6): 60302-060302.
[11]
ZHU Zhi-Ying;YU Hong-Wei. Accelerated Multi-Level Atoms in an Electromagnetic Vacuum and Fulling--Davies--Unruh Effect [J]. 中国物理快报, 2008, 25(5): 1575-1578.
[12]
JING Hui. Generation of Coherent Trimers from Bose-Condensed Atoms via a Generalized Stimulated Raman Adiabatic Passage [J]. 中国物理快报, 2008, 25(3): 847-849.
[13]
JING Hui;GENG Zhen-Duo. Efimov Superchemistry: Quantum Dynamical Theory for Coherent Atom--Trimer Conversion in a Repulsive Atomic Bose--Einstein Condensate [J]. 中国物理快报, 2008, 25(3): 850-853.
[14]
ZHAO Yan;SHAO Cheng-Gang;LUO Jun. Finite Temperature Casimir Effect for Corrugated Plates [J]. 中国物理快报, 2006, 23(11): 2928-2931.
[15]
SHU Wei-Xing;YU Hong-Wei;REN Zhong-Zhou;WU Pu-Xun;LI Fei. Lower Bounds on Negative Energy Densities for the Scalar Field in Flat Spacetime [J]. 中国物理快报, 2006, 23(1): 25-28.