$${\widehat{Z}}$$ at Large N: From Curve Counts to Quantum Modularity

Ekholm, Tobias; Gruen, Angus; Gukov, Sergei; Kucharski, Piotr; Park, Sunghyuk; Sułkowski, Piotr

doi:10.1007/s00220-022-04469-9

$$$${\widehat{Z}}$$$$ at Large N: From Curve Counts to Quantum Modularity

Journal Article · 12 August 2022 · Communications in Mathematical Physics

DOI:https://doi.org/10.1007/s00220-022-04469-9· OSTI ID:2420110

Ekholm, Tobias ^[1]; ; Gukov, Sergei; Kucharski, Piotr; Park, Sunghyuk; Sułkowski, Piotr

OSTI

Not provided.

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0011632

OSTI ID:: 2420110

Journal Information:: Communications in Mathematical Physics, Journal Name: Communications in Mathematical Physics Journal Issue: 1 Vol. 396; ISSN 0010-3616

Publisher:: Springer

Country of Publication:: United States

Language:: English

References (39)

Orientifolds and the refined topological string Aganagic, Mina; Schaeffer, Kevin Journal of High Energy Physics, Vol. 2012, Issue 9 https://doi.org/10.1007/JHEP09(2012)084	journal	September 2012
Knots-quivers correspondence Kucharski, Piotr; Reineke, Markus; Stošić, Marko Advances in Theoretical and Mathematical Physics, Vol. 23, Issue 7 https://doi.org/10.4310/ATMP.2019.v23.n7.a4	journal	January 2019
Polynomial invariants for smooth four-manifolds Donaldson, S. K. Topology, Vol. 29, Issue 3 https://doi.org/10.1016/0040-9383(90)90001-Z	journal	January 1990
Plane curves associated to character varieties of 3-manifolds Cooper, D.; Culler, M.; Gillet, H. Inventiones Mathematicae, Vol. 118, Issue 1 https://doi.org/10.1007/BF01231526	journal	December 1994
Large color R-matrix for knot complements and strange identities Park, Sunghyuk Journal of Knot Theory and Its Ramifications, Vol. 29, Issue 14 https://doi.org/10.1142/S0218216520500972	journal	December 2020
Topological strings, D-model, and knot contact homology Vafa, Cumrun; Aganagic, Mina; Ekholm, Tobias Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 4 https://doi.org/10.4310/ATMP.2014.v18.n4.a3	journal	January 2014
Volume conjecture: refined and categorified Awata, Hidetoshi; Fuji, Hiroyuki; Gukov, Sergei Advances in Theoretical and Mathematical Physics, Vol. 16, Issue 6 https://doi.org/10.4310/ATMP.2012.v16.n6.a3	journal	January 2012
BPS states, knots, and quivers Kucharski, Piotr; Reineke, Markus; Stošić, Marko Physical Review D, Vol. 96, Issue 12 https://doi.org/10.1103/PhysRevD.96.121902	journal	December 2017
Asymptotic expansions of the Witten–Reshetikhin–Turaev invariants of mapping tori I Andersen, Jørgen; Petersen, William Transactions of the American Mathematical Society, Vol. 372, Issue 8 https://doi.org/10.1090/tran/7740	journal	December 2018
Knots, BPS States, and Algebraic Curves Garoufalidis, Stavros; Kucharski, Piotr; Sułkowski, Piotr Communications in Mathematical Physics, Vol. 346, Issue 1 https://doi.org/10.1007/s00220-016-2682-z	journal	July 2016
On the Melvin-Morton-Rozansky conjecture Bar-Natan, Dror; Garoufalidis, Stavros Inventiones Mathematicae, Vol. 125, Issue 1 https://doi.org/10.1007/s002220050070	journal	May 1996
The UniversalR-Matrix, Burau Representation, and the Melvin–Morton Expansion of the Colored Jones Polynomial Rozansky, L. Advances in Mathematics, Vol. 134, Issue 1 https://doi.org/10.1006/aima.1997.1661	journal	March 1998
Quantum modular forms and plumbing graphs of 3-manifolds Bringmann, Kathrin; Mahlburg, Karl; Milas, Antun Journal of Combinatorial Theory, Series A, Vol. 170 https://doi.org/10.1016/j.jcta.2019.105145	journal	February 2020
A contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds, I Rozansky, L. Communications in Mathematical Physics, Vol. 175, Issue 2 https://doi.org/10.1007/BF02102409	journal	January 1996
Super-A-polynomials for twist knots Nawata, Satoshi; Ramadevi, P. Journal of High Energy Physics, Vol. 2012, Issue 11 https://doi.org/10.1007/JHEP11(2012)157	journal	November 2012
Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants Gukov, Sergei; Hsin, Po-Shen; Nakajima, Hiraku Journal of Geometry and Physics, Vol. 168 https://doi.org/10.1016/j.geomphys.2021.104311	journal	October 2021
Knot invariants and topological strings Ooguri, Hirosi; Vafa, Cumrun Nuclear Physics B, Vol. 577, Issue 3 https://doi.org/10.1016/S0550-3213(00)00118-8	journal	June 2000
On the characteristic and deformation varieties of a knot Garoufalidis, Stavros Conference on the Topology of Manifolds of Dimensions 3 and 4, Proceedings of the Casson Fest https://doi.org/10.2140/gtm.2004.7.291	conference	September 2004
Triply-Graded link Homology and Hochschild Homology of Soergel Bimodules Khovanov, Mikhail International Journal of Mathematics, Vol. 18, Issue 08 https://doi.org/10.1142/S0129167X07004400	journal	September 2007
Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc Katz, Sheldon; Liu, Chiu-Chu Melissa Advances in Theoretical and Mathematical Physics, Vol. 5, Issue 1 https://doi.org/10.4310/ATMP.2001.v5.n1.a1	journal	January 2001
3d modularity Cheng, Miranda C. N.; Chun, Sungbong; Ferrari, Francesca Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/JHEP10(2019)010	journal	October 2019
3d-3d correspondence for mapping tori Chun, Sungbong; Gukov, Sergei; Park, Sunghyuk Journal of High Energy Physics, Vol. 2020, Issue 9 https://doi.org/10.1007/JHEP09(2020)152	journal	September 2020
Khovanov-Rozansky Homology and Topological Strings Gukov, Sergei; Schwarz, Albert; Vafa, Cumrun Letters in Mathematical Physics, Vol. 74, Issue 1 https://doi.org/10.1007/s11005-005-0008-8	journal	October 2005
The Topological Vertex Aganagic, Mina; Klemm, Albrecht; Mari�o, Marcos Communications in Mathematical Physics, Vol. 254, Issue 2 https://doi.org/10.1007/s00220-004-1162-z	journal	September 2004
3d analogs of Argyres-Douglas theories and knot homologies Fuji, Hiroyuki; Gukov, Sergei; Stošić, Marko Journal of High Energy Physics, Vol. 2013, Issue 1 https://doi.org/10.1007/JHEP01(2013)175	journal	January 2013
BPS invariants for Seifert manifolds Chung, Hee-Joong Journal of High Energy Physics, Vol. 2020, Issue 3 https://doi.org/10.1007/JHEP03(2020)113	journal	March 2020
The refined topological vertex Iqbal, Amer; Kozçaz, Can; Vafa, Cumrun Journal of High Energy Physics, Vol. 2009, Issue 10 https://doi.org/10.1088/1126-6708/2009/10/069	journal	October 2009
Gromov–Witten theory and Donaldson–Thomas theory, I Maulik, D.; Nekrasov, N.; Okounkov, A. Compositio Mathematica, Vol. 142, Issue 05 https://doi.org/10.1112/S0010437X06002302	journal	September 2006
Fivebranes and 3-manifold homology Gukov, Sergei; Putrov, Pavel; Vafa, Cumrun Journal of High Energy Physics, Vol. 2017, Issue 7 https://doi.org/10.1007/JHEP07(2017)071	journal	July 2017
Multi-cover skeins, quivers, and 3d $$ \mathcal{N} $$ = 2 dualities Ekholm, Tobias; Kucharski, Piotr; Longhi, Pietro Journal of High Energy Physics, Vol. 2020, Issue 2 https://doi.org/10.1007/JHEP02(2020)018	journal	February 2020
Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial Gukov, Sergei Communications in Mathematical Physics, Vol. 255, Issue 3 https://doi.org/10.1007/s00220-005-1312-y	journal	March 2005
The coloured Jones function Melvin, P. M.; Morton, H. R. Communications in Mathematical Physics, Vol. 169, Issue 3 https://doi.org/10.1007/BF02099310	journal	May 1995
Super-A-polynomial for knots and BPS states Fuji, Hiroyuki; Gukov, Sergei; Sułkowski, Piotr Nuclear Physics B, Vol. 867, Issue 2 https://doi.org/10.1016/j.nuclphysb.2012.10.005	journal	February 2013
Open string instantons and relative stable morphisms Li, Jun; Song, Yun S. Advances in Theoretical and Mathematical Physics, Vol. 5, Issue 1 https://doi.org/10.4310/ATMP.2001.v5.n1.a3	journal	January 2001
The Superpolynomial for Knot Homologies Dunfield, Nathan M.; Gukov, Sergei; Rasmussen, Jacob Experimental Mathematics, Vol. 15, Issue 2 https://doi.org/10.1080/10586458.2006.10128956	journal	January 2006
BPS counting for knots and combinatorics on words Kucharski, Piotr; Sułkowski, Piotr Journal of High Energy Physics, Vol. 2016, Issue 11 https://doi.org/10.1007/JHEP11(2016)120	journal	November 2016
A-polynomial, B-model, and quantization Gukov, Sergei; Sulkowski, Piotr Journal of High Energy Physics, Vol. 2012, Issue 2 https://doi.org/10.1007/JHEP02(2012)070	journal	February 2012
Physics and Geometry of Knots-Quivers Correspondence Ekholm, Tobias; Kucharski, Piotr; Longhi, Pietro Communications in Mathematical Physics, Vol. 379, Issue 2 https://doi.org/10.1007/s00220-020-03840-y	journal	September 2020
A new polynomial invariant of knots and links Freyd, P.; Yetter, D.; Hoste, J. Bulletin of the American Mathematical Society, Vol. 12, Issue 2 https://doi.org/10.1090/S0273-0979-1985-15361-3	journal	April 1985

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