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TMF, 2010, Volume 165, Number 3, Pages 503–542 (Mi tmf6590)  

This article is cited in 16 scientific papers (total in 16 papers)

Calculations in conformal theory needed for verifying the Alday–Gaiotto–Tachikawa hypothesis

A. D. Mironovab, S. A. Mironovcb, A. Yu. Morozovb, A. A. Morozovcb

a Lebedev Physical Institute, RAS, Moscow, Russia
b Institute for Theoretical and Experimental Physics, Moscow
c Lomonosov Moscow State University, Moscow, Russia

Abstract: Explicitly verifying the Alday–Gaiotto–Tachikawa (AGT) relation between the conformal blocks controlled by the $W_N$ symmetry and $U(N)$ Nekrasov functions requires knowing the Shapovalov matrix and various triple correlators for $W$-algebra descendants. We collect the simplest expressions of this type for $N=3$ and for the two lowest descendant levels together with the detailed derivations, which can now be computerized and used in more general studies of conformal blocks and AGT relations at higher levels.

Keywords: two-dimensional conformal theory, supersymmetric gauge theory


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English version:
Theoretical and Mathematical Physics, 2010, 165:3, 1662–1698

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Citation: A. D. Mironov, S. A. Mironov, A. Yu. Morozov, A. A. Morozov, “Calculations in conformal theory needed for verifying the Alday–Gaiotto–Tachikawa hypothesis”, TMF, 165:3 (2010), 503–542; Theoret. and Math. Phys., 165:3 (2010), 1662–1698

Citation in format AMSBIB
\by A.~D.~Mironov, S.~A.~Mironov, A.~Yu.~Morozov, A.~A.~Morozov
\paper Calculations in conformal theory needed for verifying the~Alday--Gaiotto--Tachikawa~hypothesis
\jour TMF
\yr 2010
\vol 165
\issue 3
\pages 503--542
\jour Theoret. and Math. Phys.
\yr 2010
\vol 165
\issue 3
\pages 1662--1698

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    This publication is cited in the following articles:
    1. 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, 32 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Mironov A., Morozov A., Shakirov Sh., Smirnov A., “Proving AGT conjecture as HS duality: extension to five dimensions”, Nuclear Phys. B, 855:1 (2012), 128–151  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. A. Yu. Morozov, “Challenges of $\beta$-deformation”, Theoret. and Math. Phys., 173:1 (2012), 1417–1437  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    4. 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, ed. Rodrigues W. Kerner R. Pires G. Pinheiro C., Amer. Inst. Physics, 2012, 189–211  crossref  adsnasa  isi  scopus
    5. 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
    6. Anokhina A. Morozov A., “Towards 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  scopus
    7. Morozov A. Smirnov A., “Towards the Proof of AGT Relations With the Help of the Generalized Jack Polynomials”, Lett. Math. Phys., 104:5 (2014), 585–612  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. H. Itoyama, A. D. Mironov, A. Yu. Morozov, “Matching branches of a nonperturbative conformal block at its singularity divisor”, Theoret. and Math. Phys., 184:1 (2015), 891–923  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. 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
    10. 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
    11. Morozov A.A., “The properties of conformal blocks, the AGT hypothesis, and knot polynomials”, Phys. Part. Nuclei, 47:5 (2016), 775–837  crossref  mathscinet  isi  elib  scopus
    12. Awata H. Kanno H. Matsumoto T. Mironov A. Morozov A. Morozov A. Ohkubo Yu. Zenkevich Y., “Explicit examples of DIM constraints for network matrix models”, J. High Energy Phys., 2016, no. 7, 103  crossref  mathscinet  zmath  isi  elib  scopus
    13. Mironov A., Morozov A., Zenkevich Y., “On elementary proof of AGT relations from six dimensions”, Phys. Lett. B, 756 (2016), 208–211  crossref  isi  elib  scopus
    14. Carlsson E., “AGT and the Segal–Sugawara construction”, J. Math. Phys., 58:1 (2017), 011703  crossref  mathscinet  zmath  isi  scopus
    15. Morozov A., “On Exclusive Racah Matrices (S)Over-Bar For Rectangular Representations”, Phys. Lett. B, 793 (2019), 116–125  crossref  isi
    16. A. Yu. Morozov, “Cut-and-join operators and Macdonald polynomials from the 3-Schur functions”, Theoret. and Math. Phys., 200:1 (2019), 938–965  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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