Framed knots at large N

By Marcos Mariño, C. Vafa. 2001

226 citations recorded by the source corpus.

We study the framing dependence of the Wilson loop observable of U(N) ChernSimons gauge theory at large N. Using proposed geometrical large N dual, this leads to a direct computation of certain topological string amplitudes in a closed form. This yields new formulae for intersection numbers of cohomology classes on moduli of Riemann surfaces with punctures (including all the amplitudes of pure topological gravity in two dimensions). The reinterpretation of these computations in terms of BPS degeneracies of domain walls leads to novel integrality predictions for these amplitudes. Moreover we find evidence that large N dualities are more naturally formulated in the context of U(N) gauge theories rather than SU(N).

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b3986f2ee9403f8e66ac2d34171729990abf6b8f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Marcos Mariño
2. Sergei Gukov
3. C. Vafa
4. B. Eynard
5. R. Pandharipande
6. A. Okounkov
7. Tudor Dimofte
8. E. Witten

In Nuclear and High Energy Physics

1. Marcos Mariño
2. C. Vafa
3. Sergei Gukov
4. E. Witten
5. D. Gaiotto
6. N. Seiberg
7. Tudor Dimofte
8. A. Klemm

In Statistical and Nonlinear Physics

1. Marcos Mariño
2. E. Witten
3. N. Seiberg
4. C. Vafa
5. D. Gaiotto
6. Sergei Gukov
7. B. Eynard
8. A. Klemm

Citations in the corpus

• A mathematical theory of the topological vertex (2004, background): “[2] M. Aganagic, M. Marino, C. Vafa, All loop topological string amplitudes from Chern-Simons theory, Comm. Math.”
• Hurwitz numbers, matrix models and enumerative geometry (2007, methodology): “For instance, it was first conjectured in [ MV ], and then proved in [LLZ, OP3], that the open amplitudes can be written explicitly in terms of Hodge integrals, paralleling the ELSV formula for Hurwitz numbers.”
• The local Donaldson–Thomas theory of curves (2005, methodology): “play a basic role in the proof of the GW/DT correspondence for all 3-folds. The 1-legged equivariant vertex (ii) contains the Calabi-Yau 1-legged vertex governed by the Gopakumar-Marin˜o-Vafa formula [17, 21, 27] as a special 4 case. The computation of the 1-legged equivariant vertex may be viewed a”
• Generalized global symmetries (2014, background): “The required level for the U(1) theory is well-known [42, 43], but can also be understood as due to an ’t Hooft anomaly cancellation: we are gauging composite U1 operators which”
• D-brane charges in five-brane backgrounds (2001, background): “see for example [53, 54 ] for computations where it is automatically included.”
• Torus Knots and Mirror Symmetry (2011, methodology): “As we will show in this paper, the B-model geometry corresponding to a (Q,P ) torus knot is simply given by a general Sl(2,Z) transformation of the spectral curve describing the resolved conifold.”
• Worldsheet derivation of a large N duality (2002, background): “It was pointed out in [12] that, in order to fix the framing ambiguity of the loops, one needs to move the probe D branes off from the base S(3), adding mass to the open string stretched to the probe D branes and the ones wrapping on the S(3).”
• Computation of Open Gromov–Witten Invariants for Toric Calabi–Yau 3-Folds by Topological Recursion, a Proof of the BKMP Conjecture (2012, methodology): “51) is the Mariño–Vafa formula for the topological vertex [45, 43, 42], i.”
• The Topological Vertex (2003, unknown): “(3.7)”
• Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds (2008, background): “e of [1] was shown to exactly compute the Donaldson-Thomas series ofX. By the GW/DTcorrespondence of Theorem 1, the two theories coincide. The 1-leg version of the topological vertex appeared first in [21] and was proven in [19, 28]. The 2-leg case was proven in [20]. Finally, an evaluation of the Gr”
• Open string amplitudes and large order behavior in topological string theory (2006, background): “Finally, we recall that open topological string amplitudes on Calabi–Yau manifolds have an underlying integrality structure first obtained in [64] and further refined in [48, 56 ].”
• Chern-Simons theory and topological strings (2004, unknown): “Maulik et al. (2003) have shown that, when X = C(3) (so that ZDT only depends on q), the DonaldsonThomas partition function naturally depends on three sets of representations, and agrees indeed with the topological vertex CR1R2R3(q), where q in (7.”
• All Loop Topological String Amplitudes from Chern-Simons Theory (2002, methodology): “Various aspects of the duality were studied in [3,4,5,6,7,8,9,10] from different points of view.”
• Hodge integrals and invariants of the unknot (2003, methodology): “s a q-analog, or trigonometric deformation, of the ELSV formula. The formula is based upon the conjectural ChernSimons/string duality of Gopakumar and Vafa [7] applied to the case of the unknot in S3 [14]. Hodge integrals enter via a heuristic localization computation of Katz and Liu of the correspo”
• A Proof of a Conjecture of Marino-Vafa on Hodge Integrals (2003, methodology): “Therefore, the Mariño-Vafa formula (1) follows from the following theorem.”
• Vortex Counting and Lagrangian 3-Manifolds (2010, background): “ve dimensions. Its discrete coupling corresponds to the framing of the Lagrangian brane M: a choice of IR regularization that compacties M and is needed to properly dene the BPS generating function [35, 36]. Both of these discrete parameters disappear in the homological limit !0. { 24 { 3.2 Vortices”
• Invariants of spectral curves and intersection theory of moduli spaces of complex curves (2011, methodology): “24) whose right hand side is the famous Mariño–Vafa formula [22].”