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TMF, 2012, Volume 172, Number 1, Pages 73–99 (Mi tmf6930)  

This article is cited in 21 scientific papers (total in 21 papers)

Three-dimensional extensions of the Alday–Gaiotto–Tachikawa relation

D. V. Galakhovab, A. D. Mironovca, A. Yu. Morozova, A. V. Smirnova

a Institute for Theoretical and Experimental Physics, Moscow, Russia
b Moscow Institute of Physics and Technology, Dolgoprudny, Russia
c Lebedev Physical Institute, RAS, Moscow, Russia

Abstract: An extension of the two-dimensional (2d) Alday–Gaiotto–Tachikawa (AGT) relation to three dimensions starts from relating the theory on the domain wall between some two $S$-dual supersymmetric Yang–Mills (SYM) models to the 3d Chern–Simons (CS) theory. The simplest case of such a relation would presumably connect traces of the modular kernels in 2d conformal theory with knot invariants. Indeed, the two quantities are very similar, especially if represented as integrals of quantum dilogarithms. But there are also various differences, especially in the “conservation laws” for the integration variables holding for the monodromy traces but not for the knot invariants. We also consider another possibility: interpreting knot invariants as solutions of the Baxter equations for the relativistic Toda system. This implies another AGT-like relation: between the 3d CS theory and the Nekrasov–Shatashvili limit of the 5d SYM theory.

Keywords: Alday–Gaiotto–Tachikawa relation, Chern–Simons theory, knot invariant

DOI: https://doi.org/10.4213/tmf6930

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English version:
Theoretical and Mathematical Physics, 2012, 172:1, 939–962

Bibliographic databases:

Received: 09.07.2011

Citation: D. V. Galakhov, A. D. Mironov, A. Yu. Morozov, A. V. Smirnov, “Three-dimensional extensions of the Alday–Gaiotto–Tachikawa relation”, TMF, 172:1 (2012), 73–99; Theoret. and Math. Phys., 172:1 (2012), 939–962

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Yu. Morozov, “Challenges of $\beta$-deformation”, Theoret. and Math. Phys., 173:1 (2012), 1417–1437  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. A. Mironov, A. Morozov, “Equations on knot polynomials and 3d/5d duality”, Sixth International School on Field Theory and Gravitation-2012, AIP Conf. Proc., 1483, ed. W. Rodrigues, R. Kerner, G. Pires, C. Pinheiro, Amer. Inst. Physics, 2012, 189–211  crossref  adsnasa  isi
    3. D. Galakhov, A. Mironov, A. Morozov, “$S$-duality as a $\beta$-deformed Fourier transform”, J. High Energy Phys., 2012, no. 8, 067, 27 pp.  crossref  mathscinet  isi  elib
    4. 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
    5. Yu. Terashima, M. Yamazaki, “Semiclassical analysis of the 3d/3d relation”, Phys. Rev. D, 88:2 (2013), 026011  crossref  adsnasa  isi  elib
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    7. H. Itoyama, A. Mironov, A. Morozov, A. N. D. Morozov, “Eigenvalue hypothesis for Racah matrices and HOMFLY polynomials for 3-strand knots in any symmetric and antisymmetric representations”, Int. J. Mod. Phys. A, 28:3-4, SI (2013), 1340009  crossref  mathscinet  zmath  adsnasa  isi  elib
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    10. I. Gahramanov, H. Rosengren, “A new pentagon identity for the tetrahedron index”, J. High Energy Phys., 2013, no. 11, 128  crossref  isi
    11. A. S. Anokhina, A. A. Morozov, “Cabling procedure for the colored HOMFLY polynomials”, Theoret. and Math. Phys., 178:1 (2014), 1–58  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. V. Dolotin, A. Morozov, “Introduction to Khovanov homologies. III: a new and simple tensor-algebra construction of Khovanov-Rozansky invariants”, Nuclear Phys. B, 878 (2014), 12–81  crossref  mathscinet  zmath  adsnasa  isi
    13. A. Mironov, A. Morozov, A. Morozov, “On colored HOMFLY polynomials for twist knots”, Mod. Phys. Lett. A, 29:34 (2014), 1450183  crossref  zmath  adsnasa  isi
    14. A. Anokhina, A. Morozov, “Towards $\mathscr R$-matrix construction of Khovanov-Rozansky polynomials I: primary $T$-deformation of HOMFLY”, J. High Energy Phys., 2014, no. 7, 063  crossref  mathscinet  zmath  isi  elib
    15. D. M. Galakhov, A. D. Mironov, A. Yu. Morozov, “$SU(2)/SL(2)$ knot invariants and Kontsevich–Soibelman monodromies”, Theoret. and Math. Phys., 187:2 (2016), 678–694  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    16. A. A. Morozov, “The properties of conformal blocks, the AGT hypothesis, and knot polynomials”, Phys. Part. Nuclei, 47:5 (2016), 775–837  crossref  mathscinet  isi  elib  scopus
    17. A. Smirnov, “On the instanton $R$-matrix”, Commun. Math. Phys., 345:3 (2016), 703–740  crossref  mathscinet  zmath  isi  elib  scopus
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    19. A. Nedelin, F. Nieri, M. Zabzine, “$q$-Virasoro modular double and 3d partition functions”, Commun. Math. Phys., 353:3 (2017), 1059–1102  crossref  mathscinet  zmath  isi
    20. N. Nekrasov, V. Pestun, S. Shatashvili, “Quantum geometry and quiver gauge theories”, Commun. Math. Phys., 357:2 (2018), 519–567  crossref  mathscinet  zmath  isi
    21. D. N. Bozkurt, I. B. Gahramanov, “Pentagon identities arising in supersymmetric gauge theory computations”, Theoret. and Math. Phys., 198:2 (2019), 189–196  mathnet  crossref  crossref  adsnasa  isi  elib
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