Teoreticheskaya i Matematicheskaya Fizika
General information
Latest issue
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS


Personal entry:
Save password
Forgotten password?

TMF, 2007, Volume 150, Number 2, Pages 179–192 (Mi tmf5972)  

This article is cited in 57 scientific papers (total in 57 papers)

$M$-Theory of Matrix Models

A. S. Alexandrova, A. D. Mironovba, A. Yu. Morozova

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: Small $M$-theories incorporate various models representing a unified family in the same way that the $M$-theory incorporates a variety of superstring models. We consider this idea applied to the family of eigenvalue matrix models: their $M$-theory unifies various branches of the Hermitian matrix model (including the Dijkgraaf–Vafa partition functions) with the Kontsevich $\tau$-function. Moreover, the corresponding duality relations are reminiscent of instanton and meron decompositions, familiar from the Yang–Mills theory.

Keywords: string theory, matrix model, duality

DOI: https://doi.org/10.4213/tmf5972

Full text: PDF file (544 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2007, 150:2, 153–164

Bibliographic databases:

Received: 01.05.2006

Citation: A. S. Alexandrov, A. D. Mironov, A. Yu. Morozov, “$M$-Theory of Matrix Models”, TMF, 150:2 (2007), 179–192; Theoret. and Math. Phys., 150:2 (2007), 153–164

Citation in format AMSBIB
\by A.~S.~Alexandrov, A.~D.~Mironov, A.~Yu.~Morozov
\paper $M$-Theory of Matrix Models
\jour TMF
\yr 2007
\vol 150
\issue 2
\pages 179--192
\jour Theoret. and Math. Phys.
\yr 2007
\vol 150
\issue 2
\pages 153--164

Linking options:
  • http://mi.mathnet.ru/eng/tmf5972
  • https://doi.org/10.4213/tmf5972
  • http://mi.mathnet.ru/eng/tmf/v150/i2/p179

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Alexandrov A., Mironov A., Morozov A., “BGWM as second constituent of complex matrix model”, Journal of High Energy Physics, 2009, no. 12, 053, 50 pp.  crossref  mathscinet  isi  scopus
    2. Morozov A., Shakirov Sh., “Exact 2-point function in Hermitian matrix model”, Journal of High Energy Physics, 2009, no. 12, 003, 33 pp.  crossref  mathscinet  isi  scopus
    3. Morozov A., Shakirov Sh., “On equivalence of two Hurwitz matrix models”, Mod. Phys. Lett. A, 24:33 (2009), 2659–2666  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Alexandrov A., Mironov A., Morozov A., Putrov P., “Partition functions of matrix models as the first special functions of string theory II: Kontsevich model”, Int. J. Mod. Phys. A, 24:27 (2009), 4939–4998  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Eynard B., Orantin N., “Topological recursion in enumerative geometry and random matrices”, J. Phys. A, 42:29 (2009), 293001, 117 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    6. A. Yu. Morozov, “Unitary integrals and related matrix models”, Theoret. and Math. Phys., 162:1 (2010), 1–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Mironov A., Morozov A., Shakirov Sh., “Matrix model conjecture for exact BS periods and Nekrasov functions”, Journal of High Energy Physics, 2010, no. 2, 030  crossref  mathscinet  zmath  isi  scopus
    8. Morozov A., Shakirov Sh., “The matrix model version of AGT conjecture and CIV-DV prepotential”, Journal of High Energy Physics, 2010, no. 8, 066  crossref  mathscinet  zmath  isi  scopus
    9. Mironov A., Morozov A., Shakirov Sh., “Conformal blocks as Dotsenko-Fateev integral discriminants”, Internat. J. Modern Phys. A, 25:16 (2010), 3173–3207  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. Mironov A., Morozov A., “Nekrasov functions and exact Bohr-Sommerfeld integrals”, Journal of High Energy Physics, 2010, no. 4, 040  crossref  mathscinet  zmath  isi  scopus
    11. A. D. Mironov, A. Yu. Morozov, S. M. Natanzon, “Complete set of cut-and-join operators in the Hurwitz–Kontsevich theory”, Theoret. and Math. Phys., 166:1 (2011), 1–22  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    12. Mironov A., Morozov A., Shakirov Sh., “A direct proof of AGT conjecture at beta=1”, Journal of High Energy Physics, 2011, no. 2, 067  crossref  mathscinet  zmath  isi  scopus
    13. Mironov A., Morozov A., Shakirov Sh., “Brezin-Gross-Witten model as “pure gauge” limit of Selberg integrals”, Journal of High Energy Physics, 2011, no. 3, 102  crossref  mathscinet  zmath  isi  scopus
    14. Mironov A., Morozov A., Morozov A., “Conformal blocks and generalized Selberg integrals”, Nuclear Phys. B, 843:2 (2011), 534–557  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    15. Alexandrov A., “Cut-and-Join Operator Representation for Kontsevich–Witten Tau-Function”, Modern Phys. Lett. A, 26:29 (2011), 2193–2199  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    16. Alexandrov A., “Matrix models for random partitions”, Nuclear Phys. B, 851:3 (2011), 620–650  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    17. Marshakov A., Mironov A., Morozov A., “On AGT relations with surface operator insertion and a stationary limit of beta-ensembles”, J. Geom. Phys., 61:7 (2011), 1203–1222  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    18. Mironov A., Morozov A., Shakirov Sh., “Towards a Proof of AGT Conjecture By Methods of Matrix Models”, Internat. J. Modern Phys. A, 27:1 (2012), 1230001  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    19. A. D. Mironov, A. Yu. Morozov, A. V. Popolitov, Sh. R. Shakirov, “Resolvents and Seiberg–Witten representation for a Gaussian $\beta$-ensemble”, Theoret. and Math. Phys., 171:1 (2012), 505–522  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    20. D. V. Galakhov, A. D. Mironov, A. Yu. Morozov, A. V. Smirnov, “Three-dimensional extensions of the Alday–Gaiotto–Tachikawa relation”, Theoret. and Math. Phys., 172:1 (2012), 939–962  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    21. JETP Letters, 95:11 (2012), 586–593  mathnet  crossref  isi  elib  elib
    22. A. Yu. Morozov, “Challenges of $\beta$-deformation”, Theoret. and Math. Phys., 173:1 (2012), 1417–1437  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    23. Mironov A., Morozov A., “Equations on knot polynomials and 3D/5D duality”, Sixth International School on Field Theory and Gravitation-2012, AIP Conf. Proc., 1483, eds. Rodrigues W., Kerner R., Pires G., Pinheiro C., Amer. Inst. Physics, 2012, 189–211  crossref  adsnasa  isi  scopus
    24. Alexandrov A., “From Hurwitz to Kontsevich–Witten via Virasoro”, 7th International Conference on Quantum Theory and Symmetries (QTS7), Journal of Physics Conference Series, 343, IOP Publishing Ltd, 2012, 012009  crossref  adsnasa  isi  scopus
    25. Galakhov D., Mironov A., Morozov A., “S-duality as a $\beta$-deformed Fourier transform”, J. High Energy Phys., 2012, no. 8, 067  crossref  mathscinet  isi  elib  scopus
    26. Itoyama H., Mironov A., Morozov A., Morozov A., “Character expansion for HOMFLY polynomials III. All 3-strand braids in the first symmetric representation”, Internat. J. Modern Phys. A, 27:19 (2012), 1250099  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    27. Itoyama H., Mironov A., Morozov A., Morozov A., “HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations”, J. High Energy Phys., 2012, no. 7, 131  crossref  mathscinet  isi  elib  scopus
    28. Mironov A., Morozov A., Zakirova Z., “Comment on integrability in Dijkgraaf-Vafa $\beta$-ensembles”, Phys. Lett. B, 711:3-4 (2012), 332–335  crossref  mathscinet  adsnasa  isi  elib  scopus
    29. Fuji H., Gukov S., Sulkowski P., Awata H., “Volume Conjecture: Refined and Categorified”, Adv. Theor. Math. Phys., 16:6 (2012), 1669–1777  crossref  mathscinet  zmath  isi  elib
    30. Anokhina A., Mironov A., Morozov A., Morozov And., “Racah coefficients and extended HOMFLY polynomials for all 5-, 6- and 7-strand braids”, Nucl. Phys. B, 868:1 (2013), 271–313  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    31. A. D. Mironov, A. Yu. Morozov, A. V. Sleptsov, “Genus expansion of HOMFLY polynomials”, Theoret. and Math. Phys., 177:2 (2013), 1435–1470  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    32. Mironov A., Morozov A., Sleptsov A., “On Genus Expansion of Knot Polynomials and Hidden Structure of Hurwitz Tau-Functions”, Eur. Phys. J. C, 73:7 (2013), 2492  crossref  mathscinet  adsnasa  isi  scopus
    33. A. V. Popolitov, “Relation between Nekrasov functions and Bohr–Sommerfeld periods in the pure $SU(N)$ case”, Theoret. and Math. Phys., 178:2 (2014), 239–252  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    34. Alexandrov A., “From Hurwitz Numbers to Kontsevich–Witten Tau-Function: a Connection by Virasoro Operators”, Lett. Math. Phys., 104:1 (2014), 75–87  crossref  mathscinet  zmath  adsnasa  isi  scopus
    35. Sleptsov A., “Hidden Structures of Knot Invariants”, Int. J. Mod. Phys. A, 29:29 (2014), 1430063  crossref  mathscinet  zmath  adsnasa  isi  scopus
    36. Alexandrov A., Mironov A., Morozov A., Natanzon S., “On KP-Integrable Hurwitz Functions”, J. High Energy Phys., 2014, no. 11, 080  crossref  mathscinet  zmath  isi  scopus
    37. Eynard B., Kashani-Poor A.-K., Marchal O., “A Matrix Model For the Topological String i: Deriving the Matrix Model”, Ann. Henri Poincare, 15:10 (2014), 1867–1901  crossref  mathscinet  zmath  adsnasa  isi  scopus
    38. Galakhov D., Mironov A., Morozov A., “S-Duality and Modular Transformation as a Non-Perturbative Deformation of the Ordinary Pq-Duality”, J. High Energy Phys., 2014, no. 6, 050  crossref  isi  scopus
    39. Dunin-Barkowski P., Orantin N., Shadrin S., Spitz L., “Identification of the Givental Formula With the Spectral Curve Topological Recursion Procedure”, Commun. Math. Phys., 328:2 (2014), 669–700  crossref  mathscinet  zmath  adsnasa  isi  scopus
    40. Nemkov N., “S-Duality as Fourier Transform For Arbitrary Is An Element of(1), Is An Element of(2)”, J. Phys. A-Math. Theor., 47:10 (2014), 105401  crossref  mathscinet  zmath  adsnasa  isi  scopus
    41. Dartois S., “a Givental-Like Formula and Bilinear Identities For Tensor Models”, J. High Energy Phys., 2015, no. 8, 129  crossref  mathscinet  zmath  isi  elib  scopus
    42. Ding X.-M., Li Yu., Meng L., “From R-Spin Intersection Numbers To Hodge Integrals”, J. High Energy Phys., 2016, no. 1, 015  crossref  mathscinet  isi  scopus
    43. A. Yu. Morozov, “Are there $p$-adic knot invariants?”, Theoret. and Math. Phys., 187:1 (2016), 447–454  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    44. Mironov A., Morozov A., Zenkevich Y., “Ding–Iohara–Miki symmetry of network matrix models”, Phys. Lett. B, 762 (2016), 196–208  crossref  mathscinet  zmath  isi  elib  scopus
    45. Morozov A.A., “The properties of conformal blocks, the AGT hypothesis, and knot polynomials”, Phys. Part. Nuclei, 47:5 (2016), 775–837  crossref  isi  elib  scopus
    46. Morozov A., Morozov A., Popolitov A., “On ambiguity in knot polynomials for virtual knots”, Phys. Lett. B, 757 (2016), 289–302  crossref  zmath  isi  elib  scopus
    47. Gukov S., Saberi I., “Lectures on Knot Homology and Quantum Curves”, Physics and Mathematics of Link Homology, Contemporary Mathematics, 680, eds. Gukov S., Khovanov M., Walcher J., Amer Mathematical Soc, 2016, 59+  crossref  mathscinet  isi
    48. A. Yu. Morozov, A. A. Morozov, A. V. Popolitov, “Matrix model and dimensions at hypercube vertices”, Theoret. and Math. Phys., 192:1 (2017), 1039–1079  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    49. Alexandrov A., “Open Intersection Numbers and Free Fields”, Nucl. Phys. B, 922 (2017), 247–263  crossref  mathscinet  zmath  isi  scopus
    50. Aminov G. Mironov A. Morozov A., “Modular Properties of 6D (Dell) Systems”, J. High Energy Phys., 2017, no. 11, 023  crossref  mathscinet  isi  scopus
    51. Zenkevich Y., “Quantum Spectral Curve For (Q, T)-Matrix Model”, Lett. Math. Phys., 108:2 (2018), 413–424  crossref  mathscinet  zmath  isi  scopus
    52. Mironov A., Morozov A., “Sum Rules For Characters From Character-Preservation Property of Matrix Models”, J. High Energy Phys., 2018, no. 8, 163  crossref  zmath  isi  scopus
    53. Mueller S., Novaes M., “Full Perturbative Calculation of Spectral Correlation Functions For Chaotic Systems in the Unitary Symmetry Class”, Phys. Rev. E, 98:5 (2018), 052208  crossref  mathscinet  isi  scopus
    54. Dunin-Barkowski P., “Topological Recursion and Givental'S Formalism: Spectral Curves For Gromov-Witten Theories”, Topological Recursion and Its Influence in Analysis, Geometry, and Topology, Proceedings of Symposia in Pure Mathematics, 100, eds. Liu C., Mulase M., Amer Mathematical Soc, 2018, 231–295  crossref  isi
    55. Alexandrov A., “Cut-and-Join Description of Generalized Brezin-Gross-Witten Model”, Adv. Theor. Math. Phys., 22:6 (2018), 1347–1399  crossref  isi  scopus
    56. Morozov A., “On W-Representations of Beta- and Q, T-Deformed Matrix Models”, Phys. Lett. B, 792 (2019), 205–213  crossref  mathscinet  isi  scopus
    57. Andreev A., Popolitov A., Sleptsov A., Zhabin A., “Genus Expansion of Matrix Models and ? Expansion of Kp Hierarchy”, J. High Energy Phys., 2020, no. 12, 38  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:957
    Full text:264
    First page:10

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021