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TMF, 2010, Volume 164, Number 1, Pages 3–27 (Mi tmf6521)  

This article is cited in 36 scientific papers (total in 36 papers)

Combinatorial expansions of conformal blocks

A. V. Marshakovab, A. D. Mironovab, A. Yu. Morozovb

a Lebedev Physical Institute, RAS, Moscow, Russia
b Institute for Theoretical and Experimental Physics, Moscow, Russia

Abstract: A representation of Nekrasov partition functions in terms of a nontrivial two-dimensional conformal field theory was recently suggested. For a nonzero value of the deformation parameter $\epsilon=\epsilon_1+\epsilon_2$, the instanton partition function is identified with a conformal block of the Liouville theory with the central charge $c=1+6\epsilon^2/\epsilon_1\epsilon_2$. The converse of this observation means that the universal part of conformal blocks, which is the same for all two-dimensional conformal theories with nondegenerate Virasoro representations, has a nontrivial decomposition into a sum over Young diagrams that differs from the natural decomposition studied in conformal field theory. We provide some details about this new nontrivial correspondence in the simplest case of the four-point correlation functions.

Keywords: conformal theory, Seiberg–Witten theory, Nekrasov partition function

DOI: https://doi.org/10.4213/tmf6521

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English version:
Theoretical and Mathematical Physics, 2010, 164:1, 831–852

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Received: 04.11.2009

Citation: A. V. Marshakov, A. D. Mironov, A. Yu. Morozov, “Combinatorial expansions of conformal blocks”, TMF, 164:1 (2010), 3–27; Theoret. and Math. Phys., 164:1 (2010), 831–852

Citation in format AMSBIB
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    11. Itoyama H., Oota T., “$A^{(1)}_n$ affine quiver matrix model”, Nuclear Phys. B, 852:1 (2011), 336–351  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Itoyama H., Yonezawa N., “$\epsilon$-corrected Seiberg-Witten prepotential obtained from half-genus expansion in $\beta$-deformed matrix model”, Internat. J. Modern Phys. A, 26:20 (2011), 3439–3467  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    13. Taki M., “On AGT conjecture for pure super Yang-Mills and W-algebra”, J. High Energy Phys., 2011, no. 5, 038  crossref  mathscinet  zmath  isi  elib  scopus
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    18. 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
    19. Bao L., Pomoni E., Taki M., Yagi F., “M5-branes, toric diagrams and gauge theory duality”, J. High Energy Phys., 2012, no. 4, 105, 58 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    20. Cirafici M., Szabo R.J., “Curve Counting, Instantons and McKay Correspondences”, J. Geom. Phys., 72 (2013), 54–109  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    21. Gamayun O., Iorgov N., Lisovyy O., “How Instanton Combinatorics Solves Painlevé VI, V and Iiis”, J. Phys. A-Math. Theor., 46:33 (2013), 335203  crossref  mathscinet  zmath  isi  elib  scopus
    22. Bourgine J.-E., “Large N Techniques for Nekrasov Partition Functions and AGT Conjecture”, J. High Energy Phys., 2013, no. 5, 047  crossref  isi  elib  scopus
    23. 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
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    30. Morozov A. Zenkevich Y., “Decomposing Nekrasov Decomposition”, J. High Energy Phys., 2016, no. 2, 098  crossref  mathscinet  isi  scopus
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