Papers
Topics
Authors
Recent
Search
2000 character limit reached

Log topological recursion through the prism of $x-y$ swap

Published 28 Dec 2023 in math-ph, hep-th, math.AG, math.CO, and math.MP | (2312.16950v3)

Abstract: We introduce a new concept of logarithmic topological recursion that provides a patch to topological recursion in the presence of logarithmic singularities and prove that this new definition satisfies the universal $x-y$ swap relation. This result provides a vast generalization and a proof of a very recent conjecture of Hock. It also uniformly explains (and conceptually rectifies) an approach to the formulas for the $n$-point functions proposed by Hock.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (50)
  1. “Weighted Hurwitz numbers and topological recursion” In Comm. Math. Phys. 375.1, 2020, pp. 237–305 DOI: 10.1007/s00220-020-03717-0
  2. Alexander Alexandrov “KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions”, 2021 arXiv:2108.10023 [math.AG]
  3. “A universal formula for the x−y𝑥𝑦x-yitalic_x - italic_y swap in topological recursion”, 2022 arXiv:2212.00320 [math-ph]
  4. “KP integrability through the x−y𝑥𝑦x-yitalic_x - italic_y swap relation”, 2023 arXiv:2309.12176 [math-ph]
  5. Gaëtan Borot “Topological recursion and geometry” In Rev. Math. Phys. 32.10, 2020, pp. 2030007, 50 DOI: 10.1142/S0129055X20300071
  6. Gaëtan Borot, Bertrand Eynard and Nicolas Orantin “Abstract loop equations, topological recursion and new applications” In Commun. Number Theory Phys. 9.1, 2015, pp. 51–187 DOI: 10.4310/CNTP.2015.v9.n1.a2
  7. “Blobbed topological recursion: properties and applications” In Math. Proc. Cambridge Philos. Soc. 162.1, 2017, pp. 39–87 DOI: 10.1017/S0305004116000323
  8. “Taking limits in topological recursion”, 2023 arXiv:2309.01654 [math.AG]
  9. “Functional relations for higher-order free cumulants”, 2023 arXiv:2112.12184 [math.OA]
  10. “Mirror symmetry for orbifold Hurwitz numbers” In J. Differential Geom. 98.3, 2014, pp. 375–423 URL: http://projecteuclid.org/euclid.jdg/1406552276
  11. “Remodeling the B-model” In Comm. Math. Phys. 287.1, 2009, pp. 117–178 DOI: 10.1007/s00220-008-0620-4
  12. “Hurwitz numbers, matrix models and enumerative geometry” In From Hodge theory to integrability and TQFT tt*-geometry 78, Proc. Sympos. Pure Math. Amer. Math. Soc., Providence, RI, 2008, pp. 263–283 DOI: 10.1090/pspum/078/2483754
  13. Andrea Brini, Bertrand Eynard and Marcos Mariño “Torus knots and mirror symmetry” In Ann. Henri Poincaré 13.8, 2012, pp. 1873–1910 DOI: 10.1007/s00023-012-0171-2
  14. B. Bychkov, P. Dunin-Barkowski and S. Shadrin “Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursion” In European J. Combin. 90, 2020, pp. 103184, 35 DOI: 10.1016/j.ejc.2020.103184
  15. “Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type”, 2021 arXiv:2012.14723 [math-ph]
  16. “Explicit closed algebraic formulas for Orlov-Scherbin n𝑛nitalic_n-point functions” In J. Éc. Polytech., Math. 9, 2022, pp. 1121–1158 DOI: 10.5802/jep.202
  17. Leonid Chekhov, Bertrand Eynard and Nicolas Orantin “Free energy topological expansion for the 2-matrix model” In J. High Energy Phys., 2006, pp. 053, 31 DOI: 10.1088/1126-6708/2006/12/053
  18. Lin Chen “Bouchard-Klemm-Marino-Pasquetti conjecture for ℂ3superscriptℂ3\mathbb{C}^{3}blackboard_C start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT” In Topological recursion and its influence in analysis, geometry, and topology 100, Proc. Sympos. Pure Math. Amer. Math. Soc., Providence, RI, 2018, pp. 83–102 DOI: 10.1090/pspum/100/03
  19. Nitin Kumar Chidambaram, Elba Garcia-Failde and Alessandro Giacchetto “Relations on ℳ¯g,nsubscript¯ℳ𝑔𝑛\overline{\mathcal{M}}_{g,n}over¯ start_ARG caligraphic_M end_ARG start_POSTSUBSCRIPT italic_g , italic_n end_POSTSUBSCRIPT and the negative r𝑟ritalic_r-spin Witten conjecture”, 2022 arXiv:2205.15621 [math.AG]
  20. Norman Do, Oliver Leigh and Paul Norbury “Orbifold Hurwitz numbers and Eynard-Orantin invariants” In Math. Res. Lett. 23.5, 2016, pp. 1281–1327 DOI: 10.4310/MRL.2016.v23.n5.a3
  21. “Lectures on the topological recursion for Higgs bundles and quantum curves” In The geometry, topology and physics of moduli spaces of Higgs bundles 36, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. World Sci. Publ., Hackensack, NJ, 2018, pp. 103–198
  22. “The spectral curve of the Eynard-Orantin recursion via the Laplace transform” In Algebraic and geometric aspects of integrable systems and random matrices 593, Contemp. Math. Amer. Math. Soc., Providence, RI, 2013, pp. 263–315 DOI: 10.1090/conm/593/11867
  23. “Polynomiality of Hurwitz numbers, Bouchard-Mariño conjecture, and a new proof of the ELSV formula” In Adv. Math. 279, 2015, pp. 67–103 DOI: 10.1016/j.aim.2015.03.016
  24. “Cut-and-join equation for monotone Hurwitz numbers revisited” In J. Geom. Phys. 137, 2019, pp. 1–6 DOI: 10.1016/j.geomphys.2018.11.010
  25. “Polynomiality of orbifold Hurwitz numbers, spectral curve, and a new proof of the Johnson-Pandharipande-Tseng formula” In J. Lond. Math. Soc. (2) 92.3, 2015, pp. 547–565 DOI: 10.1112/jlms/jdv047
  26. “Primary invariants of Hurwitz Frobenius manifolds” In Topological recursion and its influence in analysis, geometry, and topology 100, Proc. Sympos. Pure Math. Amer. Math. Soc., Providence, RI, 2018, pp. 297–331 DOI: 10.1090/pspum/100/01768
  27. “Dubrovin’s superpotential as a global spectral curve” In J. Inst. Math. Jussieu 18.3, 2019, pp. 449–497 DOI: 10.1017/s147474801700007x
  28. “Identification of the Givental formula with the spectral curve topological recursion procedure” In Comm. Math. Phys. 328.2, 2014, pp. 669–700 DOI: 10.1007/s00220-014-1887-2
  29. “Topological recursion for the extended Ooguri-Vafa partition function of colored HOMFLY-PT polynomials of torus knots” In Adv. Theor. Math. Phys. 26.4, 2022, pp. 793–833 DOI: 10.4310/atmp.2022.v26.n4.a1
  30. “Loop equations and a proof of Zvonkine’s q⁢r𝑞𝑟qritalic_q italic_r-ELSV formula” In Ann. Sci. Éc. Norm. Supér. (4) 56.4, 2023, pp. 1199–1229 DOI: 10.24033/asens.2553
  31. “Combinatorics of loop equations for branched covers of sphere” In Int. Math. Res. Not. IMRN, 2018, pp. 5638–5662 DOI: 10.1093/imrn/rnx047
  32. “Combinatorial structure of colored HOMFLY-PT polynomials for torus knots” In Commun. Number Theory Phys. 13.4, 2019, pp. 763–826 DOI: 10.4310/cntp.2019.v13.n4.a3
  33. B. Eynard “Invariants of spectral curves and intersection theory of moduli spaces of complex curves” In Commun. Number Theory Phys. 8.3, 2014, pp. 541–588 DOI: 10.4310/CNTP.2014.v8.n3.a4
  34. “Invariants of algebraic curves and topological expansion” In Commun. Number Theory Phys. 1.2, 2007, pp. 347–452 DOI: 10.4310/CNTP.2007.v1.n2.a4
  35. “Computation of open Gromov-Witten invariants for toric Calabi-Yau 3-folds by topological recursion, a proof of the BKMP conjecture” In Comm. Math. Phys. 337.2, 2015, pp. 483–567 DOI: 10.1007/s00220-015-2361-5
  36. Bertrand Eynard “An overview of the topological recursion” In Proceedings of the International Congress of Mathematicians—Seoul 2014. Vol. III Kyung Moon Sa, Seoul, 2014, pp. 1063–1085
  37. Bertrand Eynard, Motohico Mulase and Bradley Safnuk “The Laplace transform of the cut-and-join equation and the Bouchard-Mariño conjecture on Hurwitz numbers” In Publ. Res. Inst. Math. Sci. 47.2, 2011, pp. 629–670 DOI: 10.2977/PRIMS/47
  38. “Topological recursion in enumerative geometry and random matrices” In J. Phys. A 42.29, 2009, pp. 293001, 117 DOI: 10.1088/1751-8113/42/29/293001
  39. Bohan Fang, Chiu-Chu Melissa Liu and Zhengyu Zong “On the remodeling conjecture for toric Calabi-Yau 3-orbifolds” In J. Amer. Math. Soc. 33.1, 2020, pp. 135–222 DOI: 10.1090/jams/934
  40. Alexander Hock “A simple formula for the x𝑥xitalic_x-y𝑦yitalic_y symplectic transformation in topological recursion”, 2022 arXiv:2211.08917 [math-ph]
  41. Alexander Hock “On the x𝑥xitalic_x-y𝑦yitalic_y Symmetry of Correlators in Topological Recursion via Loop Insertion Operator”, 2022 arXiv:2201.05357 [math-ph]
  42. Alexander Hock “Laplace transform of the x−y𝑥𝑦x-yitalic_x - italic_y symplectic transformation formula in Topological Recursion”, 2023 arXiv:2304.03032 [math-ph]
  43. Alexander Hock “x−y𝑥𝑦x-yitalic_x - italic_y duality in Topological Recursion for exponential variables via Quantum Dilogarithm”, 2023 arXiv:2311.11761 [math-ph]
  44. “Polynomial Relations Among Kappa Classes on the Moduli Space of Curves” In International Mathematics Research Notices, 2023, pp. rnad061 DOI: 10.1093/imrn/rnad061
  45. “Chiodo formulas for the r𝑟ritalic_r-th roots and topological recursion” In Lett. Math. Phys. 107.5, 2017, pp. 901–919 DOI: 10.1007/s11005-016-0928-5
  46. Paul Norbury “A new cohomology class on the moduli space of curves” In Geom. Topol. 27.7, 2023, pp. 2695–2761 DOI: 10.2140/gt.2023.27.2695
  47. “Gromov-Witten invariants of ℙ1superscriptℙ1\mathbb{P}^{1}blackboard_P start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT and Eynard-Orantin invariants” In Geom. Topol. 18.4, 2014, pp. 1865–1910 DOI: 10.2140/gt.2014.18.1865
  48. S. Shadrin, L. Spitz and D. Zvonkine “Equivalence of ELSV and Bouchard-Mariño conjectures for r𝑟ritalic_r-spin Hurwitz numbers” In Math. Ann. 361.3-4, 2015, pp. 611–645 DOI: 10.1007/s00208-014-1082-y
  49. Jian Zhou “Local Mirror Symmetry for One-Legged Topological Vertex”, 2009 arXiv:0910.4320 [math.AG]
  50. Jian Zhou “Topological recursions of Eynard-Orantin type for intersection numbers on moduli spaces of curves” In Lett. Math. Phys. 103.11, 2013, pp. 1191–1206 DOI: 10.1007/s11005-013-0632-7
Citations (3)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.

Sign Up for Free