×

On fermionic representation of the framed topological vertex. (English) Zbl 1388.81716

Summary: The Gromov-Witten invariants of \( {\mathbb{C}}^3 \) with branes is encoded in the topological vertex which has a very complicated combinatorial expression. A simple formula for the topological vertex was proposed by Aganagic et al. in the fermionic picture. We will propose a similar formula for the framed topological vertex and prove it in the case when there are one or two branes.

MSC:

81T45 Topological field theories in quantum mechanics
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] M. Aganagic, R. Dijkgraaf, A. Klemm, M. Mariño and C. Vafa, Topological strings and integrable hierarchies, Commun. Math. Phys.261 (2006) 451 [hep-th/0312085] [INSPIRE]. · Zbl 1095.81049 · doi:10.1007/s00220-005-1448-9
[2] M. Aganagic, A. Klemm, M. Mariño and C. Vafa, The topological vertex, Commun. Math. Phys.254 (2005) 425 [hep-th/0305132] [INSPIRE]. · Zbl 1114.81076 · doi:10.1007/s00220-004-1162-z
[3] V.G. Kac and J.W. van de Leur, The n component of KP hierarchy and representation theory, J. Math. Phys.44 (2003) 3245 [hep-th/9308137] [INSPIRE]. · Zbl 1062.37071 · doi:10.1063/1.1590055
[4] J. Li, C.-C.M. Liu, K. Liu and J. Zhou, A mathematical theory of the topological vertex, Geom. Topol.13 (2009) 527 [math/0408426] [INSPIRE]. · Zbl 1184.14084
[5] I.G. MacDonald, Symmetric functions and Hall polynomials, second edition, Claredon Press, (1995). · Zbl 0824.05059
[6] M. Mariño and C. Vafa, Framed knots at large-N , Contemp. Math.310 (2002) 185 [hep-th/0108064] [INSPIRE]. · Zbl 1042.81071 · doi:10.1090/conm/310/05404
[7] J. Zhou, A conjecture on Hodge integrals, math/0310282.
[8] J. Zhou, Localizations on moduli spaces and free field realizations of Feynman rules, math/0310283 [INSPIRE].
[9] J. Zhou, Hodge integrals and integrable hierarchies, Lett. Math. Phys.93 (2010) 55. · Zbl 1194.14080 · doi:10.1007/s11005-010-0397-1
[10] J. Zhou, Curve counting and instanton counting, math/0311237 [INSPIRE].
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.