Moscow Mathematical Journal
General information
Latest issue
Impact factor

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Mosc. Math. J.:

Personal entry:
Save password
Forgotten password?

Mosc. Math. J., 2014, Volume 14, Number 1, Pages 39–61 (Mi mmj514)  

This article is cited in 24 scientific papers (total in 24 papers)

Five dimensional gauge theories and vertex operators

Erik Carlssona, Nikita Nekrasovbcda, Andrei Okounkovde

a Simons Center for Geometry and Physics, Stony Brook NY 11794-3636 USA
b Alikhanov Institute of Theoretical and Experimental Physics, Moscow 117218 Russia
c Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette 91440 France
d Kharkevich Institute for Information Transmission Problems, Lab. 5, Moscow 127994 Russia
e Department of Mathematics, Columbia University, New York USA

Abstract: We study supersymmetric gauge theories in five dimensions, using their relation to the $K$-theory of the moduli spaces of torsion free sheaves. In the spirit of the BPS/CFT correspondence the partition function and the expectation values of the chiral, BPS protected observables are given by the matrix elements and more generally by the correlation functions in some $q$-deformed conformal field theory in two dimensions. We show that the coupling of the gauge theory to the bi-fundamental matter hypermultiplet inserts a particular vertex operator in this theory. In this way we get a generalization of the main result of a paper by E.C. and A.O. to $K$-theory. The theory of interpolating Macdonald polynomials is an important tool in our construction.

Key words and phrases: gauge theory, representation theory, symmetric group, $K$-theory, Hilbert scheme, BPS/CFT correspondence.


Full text:
References: PDF file   HTML file

Bibliographic databases:

MSC: 33D52, 14D21
Received: October 18, 2012; in revised form July 6, 2013

Citation: Erik Carlsson, Nikita Nekrasov, Andrei Okounkov, “Five dimensional gauge theories and vertex operators”, Mosc. Math. J., 14:1 (2014), 39–61

Citation in format AMSBIB
\by Erik~Carlsson, Nikita~Nekrasov, Andrei~Okounkov
\paper Five dimensional gauge theories and vertex operators
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 1
\pages 39--61

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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. N. Iorgov, O. Lisovyy, J. Teschner, “Isomonodromic tau-functions from Liouville conformal blocks”, Comm. Math. Phys., 336:2 (2015), 671–694  crossref  mathscinet  zmath  isi  elib  scopus
    2. R. J. Szabo, “$\mathcal N=2$ gauge theories, instanton moduli spaces and geometric representation theory”, J. Geom. Phys., 109 (2016), 83–121  crossref  mathscinet  zmath  isi  scopus
    3. S. Benvenuti, G. Bonelli, M. Ronzani, A. Tanzini, “Symmetry enhancements via 5d instantons, $q\mathcal W$ -algebrae and $(1,0)$ superconformal index”, J. High Energy Phys., 2016, no. 9, 053, 25 pp.  crossref  mathscinet  isi  scopus
    4. H. Awata, H. Kanno, T. Matsumoto, A. Mironov, A. Morozov, A. Morozov, Yu. Ohkubo, Y. Zenkevich, “Explicit examples of DIM constraints for network matrix models”, J. High Energy Phys., 2016, no. 7, 103, 66 pp.  crossref  mathscinet  isi  scopus
    5. A. Mironov, A. Morozov, Y. Zenkevich, “Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings”, J. High Energy Phys., 2016, no. 5, 121, 43 pp.  crossref  mathscinet  isi  scopus
    6. A. Mironov, A. Morozov, Y. Zenkevich, “On elementary proof of AGT relations from six dimensions”, Phys. Lett. B, 756 (2016), 208–211  crossref  isi  scopus
    7. A. Iqbal, B. A. Qureshi, Kh. Shabbir, “$(q,t)$ identities and vertex operators”, Modern Phys. Lett. A, 31:11 (2016), 1650065, 9 pp.  crossref  mathscinet  zmath  isi  scopus
    8. J. Qiu, L. Tizzano, J. Winding, M. Zabzine, “Modular properties of full 5D SYM partition function”, J. High Energy Phys., 2016, no. 3, 193  crossref  isi  scopus
    9. N. Nekrasov, “BPS/CFT correspondence: non-perturbative Dyson–Schwinger equations and $qq$-characters”, J. High Energy Phys., 2016, no. 3, 181  crossref  isi  scopus
    10. J. Teschner, “Exact results on $\mathcal N=2$ supersymmetric gauge theories”, dualities of sypersymmetric gauge theories, Math. Phys. Stud., Springer, Cham, 2016, 1–30  crossref  mathscinet  zmath  isi
    11. Yu. Tachikawa, “A review on instanton counting and W-algebras”, New dualities of sypersymmetric gauge theories, Math. Phys. Stud., Springer, Cham, 2016, 79–120  crossref  mathscinet  zmath  isi
    12. E. Carlsson, “AGT and the Segal–Sugawara construction”, J. Math. Phys., 58:1 (2017), 011703, 17 pp.  crossref  mathscinet  zmath  isi  scopus
    13. Ya. A. Kononov, A. Yu. Morozov, “Rectangular superpolynomials for the figure-eight knot $4_1$”, Theoret. and Math. Phys., 193:2 (2017), 1630–1646  mathnet  crossref  crossref  adsnasa  isi  elib
    14. J.-E. Bourgine, M. Fukuda, Y. Matsuo, R.-D. Zhu, “Reflection states in Ding–Iohara–Miki algebra and brane-web for D-type quiver”, J. High Energy Phys., 2017, no. 12, 015  crossref  mathscinet  isi  scopus
    15. F. Nieri, “An elliptic Virasoro symmetry in 6D”, Lett. Math. Phys., 107:11 (2017), 2147–2187  crossref  mathscinet  zmath  isi  scopus
    16. Y. Zenkevich, “Refined toric branes, surface operators and factorization of generalized Macdonald polynomials”, J. High Energy Phys., 2017, no. 9, 070  crossref  mathscinet  isi  scopus
    17. H. Awata, H. Fujino, Yu. Ohkubo, “Crystallization of deformed Virasoro algebra, Ding–Iohara–Miki algebra, and 5D AGT correspondence”, J. Math. Phys., 58:7 (2017), 071704  crossref  mathscinet  zmath  isi  scopus
    18. F. Nieri, Y. Pan, M. Zabzine, “3D mirror symmetry from $S$-duality”, Phys. Rev. D, 98:12 (2018), 126002  crossref  isi  scopus
    19. E. M. Rains, S. O. Warnaar, “A Nekrasov-Okounkov formula for Macdonald polynomials”, J. Algebr. Comb., 48:1 (2018), 1–30  crossref  mathscinet  zmath  isi  scopus
    20. E. Carlsson, F. R. Villegas, “Vertex operators and character varieties”, Adv. Math., 330 (2018), 38–60  crossref  mathscinet  zmath  isi  scopus
    21. F. Nieri, Y. Pan, M. Zabzine, “3d expansions of 5d instanton partition functions”, J. High Energy Phys., 2018, no. 4, 092  crossref  mathscinet  isi  scopus
    22. A. Barns-Graham, N. Dorey, N. Lohitsiri, D. Tong, C. Turner, “ADHM and the 4d quantum Hall effect”, J. High Energy Phys., 2018, no. 4, 040  crossref  mathscinet  isi  scopus
    23. A. Negut, “The $q$-AGT-W relations via shuffle algebras”, Commun. Math. Phys., 358:1 (2018), 101–170  crossref  mathscinet  zmath  isi  scopus
    24. Masayuki Fukuda, Yusuke Ohkubo, Jun'ichi Shiraishi, “Non-Stationary Ruijsenaars Functions for $\kappa=t^{-1/N}$ and Intertwining Operators of Ding–Iohara–Miki Algebra”, SIGMA, 16 (2020), 116, 55 pp.  mathnet  crossref
  • Moscow Mathematical Journal
    Number of views:
    This page:339

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