The refined topological vertex

By Amer Iqbal, C. Kozçaz, C. Vafa. 2007

576 citations recorded by the source corpus.

We define a refined topological vertex which depends in addition on a parameter, which physically corresponds to extending the self-dual graviphoton field strength to a more general configuration. Using this refined topological vertex we compute, using geometric engineering, a two-parameter (equivariant) instanton expansion of gauge theories which reproduce the results of Nekrasov. The refined vertex is also expected to be related to Khovanov knot invariants.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/219a094ef9ad8ace43c90a3d534c1d070876014e

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Citations in the corpus

Liouville Correlation Functions from Four-Dimensional Gauge Theories (2009, background): “This just reflects the difference in the conventions in [3] and in [10, 11] of the zero of the hypermultiplet mass.”
Matrix models, geometric engineering and elliptic genera (2003, methodology): “This partition function can also be calculated using the refined vertex formalism developed recently in [76].”
Refined Topological Vertex and Instanton Counting (2007, methodology): “The refined partition functions for the SU(2) and SU(3) geometries and their blow-up were computed in [18].”
Refined curve counting on complex surfaces (2012, background): “This fact was used in [PT2] as evidence that the niC were in fact the Gopakumar-Vafa invariants, and was exploited in [KST] to count curves on surfaces.”
Refined stable pair invariants for E-, M- and [p, q]-strings (2013, methodology): “Then the proposal in [80] for the generating function for the higher genus refined constant map contributions is”
Fivebranes and Knots (2011, methodology): “For an extension of these ideas involving the topological vertex and the Nekrasov partition function for instantons, see [61] and [52].”
Hitchin systems, N = 2 gauge theories and W-gravity (2009, methodology): “On the other han d, counting holomorphic maps points to the A-model and this suggests an interpretation of the Tod a conformal blocks as the refined topological vertex of [20].”
Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry (2009, methodology): “In a similar spirit, one can establish a relation between our surface operators in N = 2 field theories, and the D-strings employed by [16] in N = 2 string theory compactifications to give a physical interpretation to the refined open topological string amplitudes[17, 18].”
On instantons as Kaluza-Klein modes of M5-branes (2011, background): “Following the notation of [45], one finds that the instanton part of the partition function Zinst (i.”
M-Strings (2013, methodology): “The topological string partition function can be calculated using the refined topological vertex formalism [11].”
Non-perturbative effects and the refined topological string (2013, methodology): “21) of the topological string free energy [39].”
Motivic degree zero Donaldson–Thomas invariants (2009, background): “Motivated by work of Okounkov and Reshetikhin [31], in a recent paper [19], Iqbal–Kozçaz–Vafa discussed a family of q-deformations of this formula.”
Quantum geometry of refined topological strings (2011, methodology): “For the A-model, it has been proposed that the refined topological vertex, which is the one-parameter refinement of the standard topological vertex, computes the corresponding degeneracies [3].”
Refined, Motivic, and Quantum (2009, methodology): “The last term, w∞(Θ ), is obtained from a slightly modified version of the refined topological vertex of [6].”
Orbifolds of M-strings (2013, methodology): “As a main tool we will use the topological vertex and its refinement [5–7, 15, 16], to compute the degeneracy of BPS states.”
Gauge theory loop operators and Liouville theory (2009, methodology): “Progress in realizing the Nekrasov instanton partition function [11, 12] for arbitrary ǫ1 and ǫ2 have been made in topological string theory, where amplitudes sewn from a “refined” topological vertex [60, 61] were shown to reproduce Nekrasov’s partition function.”
The Ω Deformed B-model for Rigid N = 2 Theories (2011, methodology): “However, it was pointed out in [45, 46, 47, 19, 48] that the masses m̂i in the Nekrasov expansion should be redefined in terms of physical masses m̂i = mi + ǫ1 + ǫ2 2 .”
Lectures on K-theoretic computations in enumerative geometry (2015, background): “14) corresponds to the refined vertex of Iqbal, Kozcaz, and Vafa in [41].”